Bubu - Specular Soul

If you don't have Specular Soul yet but want to try her out, she is available as a Trial Operative in story chapter SP-8 "Reflection of Valor" (Main Story // Journey // Allies Revisited)

Bubu offers very high damage and some auto-aim and AoE in a good looking package, but Bubu has quite low mobility that can also lead to below-average survivability.
The game describes Bubu as a "Ballistic DPS" but she deals enough skill damage (around 25% of her base dps) that she's really more of a hybrid dps, which can make teambuilding difficult for her as she doesn't fully benefit from either purely-ballistic or purely-skill supports, and there just aren't any hybrid supports that work perfectly with her.

The Basics

Role: Main DPS
Deals Chaos Damage
Weapon Type: Dual SMG
Deals both ballistic and skill damage
( Around 2:1 Ballistic:Skill )
Mobility is below average

How to use Bubu - Specular Soul

Shoot enemies until the gauge around the centre of the screen is full
When the gauge is full, use Bubu's standard skill to gain 1 charge
When Bubu has 4 charges, use her ult
Whilst in her ult, repeatedly use Bubu's standard skill 8 times
After the 8th shot, Bubu will automatically deal AoE damage
(This can miss if there isn't an enemy directly in front of you.)
I recommend you reload here after her ult deals AoE damage.

Repeat

(This rotation takes around 16-17 seconds)

How to build Bubu - Specular Soul

Weapon: Auspice Cinders / Serrated Pines
Weapon Parts: Max ATK
Logistics Squad: Verdure
+ 10.0% Max ATK
+ 106 Alignment Index
+ 8.5% Chaos Damage
Best supports:
Vidya - Celestial Swan
Fenny - Starshine
Yao - Nightglow
Marian - Aquila
Eatchel - The Cub

Specifics:

UI

Bubu has a gauge in the centre of the screen.
The number in the centre is her "Light Crystal" value.
The circular bar around the outside charges as she gains "Optic Halo".

Basic Attack

Bubu's regular shots from her Dual SMGs charge up the "Optic Halo" around the edge of the gauge in the centre of the screen.
Each shot gains 1 Optic Halo, up to a max of 16.
Bubu needs to fully charge four times per rotation, but her Dual SMGs have an ammo capacity of 100, so hitting the 64 shots needed isn't usually that difficult.

Standard Skill - Uncharged

If you use her standard skill when the Optic Halo gauge isn't full, Bubu will do an AoE attack in front of her, dealing Chaos damage to up to 5 enemies.
This is just an AoE skill dealing skill damage to up to 5 enemies - There's nothing special about it beyond that.

This does deal 350% damage, giving it actually quite good dps for something on a 2.5s cooldown.
With its first Neuronic buff, it gains S-Energy and a 0.5s cooldown for each target it hits. This means that when hitting 5 targets Bubu can spam it indefinitely, and against smaller groups it's still very spammable.
Being able to spam this repeatedly against groups does actually give Bubu very good AoE dps - her standard damage rotation of shooting and using her ult is better against single-targets, but against large groups just spamming her standard skill is a very good option.

Note that this uncharged Standard Skill damage doesn't give or use any Light Crystals, and as such doesn't proc her Verdure logistics set, meaning that using Bubu's uncharged Standard Skill can cause the Verdure logistics buff to time out. It also doesn't proc the ATK buff from Bubu's M5 either, so it will time out if you use her uncharged skill.
As such, if you want Bubu to deal maximum single-target dps then you never want to use her Standard Skill while it's uncharged.

Standard Skill - Charged

When the Optic Halo gauge is full, you can use Bubu's Standard Skill to shoot a "Spectral Shot" at the enemy.
This Spectral Shot:

Does actually count as a shot, so for example it benefits from per-shot aptitude buffs like those from Tess - Phantasia's Support Skill.
Also counts as a skill use as well
Has auto-lock-on, meaning that provided you're looking vaguely near an enemy it can't miss.
Is a Guaranteed Crit.
Has fixed Compatibility value [of 420%]
Her 4* and 5* weapons both have a Compatibility value of 18.21%, meaning this Spectral Shot deals 30.5x the base damage of a regular shot.
Increases the "Light Crystal" value in the centre of the screen, up to a max of 4.
Note that the Spectral Shot has to deal damage to an enemy to gain this, so if it misses or hits terrain instead of an enemy then you don't gain a Light Crystal.
Inflicts 1 "Fracture Mark" on the enemy, up to a max of 24 marks per target.
These are used by her ult.
Moves Bubu a little bit.
If you aren't telling Bubu to move in a specific direction, she will instead default to moving backwards.

Ultimate Skill

When Bubu has at least 2 Light Crystals, you can use her ult to enter "Specular Realm form".
In this form, using her Ult doubles the number of Light Crystals she has, and enhances her Standard Skill shot, which consumes 1 Light Crystal per shot to also deal a "dual skill shot" (a.k.a. "extra damage") that also deals splash damage to up to 5 targets 3x times, each inflicting 2 Fracture Mark, up to 4 marks per-target.
Whilst in her ult form, her standard skill still doesn't use S-Energy or have any cooldown, but regular shots don't generate any Optic Halo.
Whilst not stated in her skill description, her Dual Skill Shot is purely ballistic damage with Weapon Compatibility fixed to 80%.

Bubu's ult ends after she runs out of Light Crystals.
You can end it early (before she runs out of Light Crytsals) by using her ult again.
When doing this, Bubu deals AoE chaos damage directly in front of her, dealing extra damage per Fracture Mark.
Note that this blast always happens directly in front of Bubu, and enemies at long range won't be affected by the blast.

Bubu's ult also ends early if she's in her ult form for more than 30s. Her ult ending this way doesn't trigger a blast.
Bubu leaving the field immediately ends her ult without triggering a blast.

Note that her ults first Neuronic gives her Specular Slash +100% Final damage if it only hits 1 target.
The Specular Slash is is the extra AoE damage. It's not that strong.
Specular Slash averages a dps of around 45% of Bubu's ATK.

The 4 Spectral Shots from her standard skill inflict 1 Fracture Mark each, for 4 total.
Bubu's ult then gives her 8 shots, each of which inflict up to 4 Fracture Mark, meaning Bubu can get to the max of 24 Fracture Mark pretty easily.

Support Skill

Bubu's support skill deals Chaos damage eight times to a single target.

With its first Neuronic buff, this inflicts Slow for 2s.
With its second Neuronic buff, this inflicts Dazed for 5s, dealing an extra 100% damage in total.

The damage of this skill is quite high for the support skill of a main dps operative, but its overall dps is still low, and like all main dps operatives you don't want to be using Bubu as a support operative.

Weapon

Auspice Cinders
Her 5* Event Weapon, and her best weapon.
+Chaos damage passive.
After using standard skill, +18% ballistic damage for 2s.
After dealing Chaos DMG with standard skill, enemies take more damage from Bubu for 2s.
This is an 18-30% damage taken bonus, which is very strong, making Auspice Cinders much stronger than Bubu's 4* weapons.
+ATK when both effects are active.
Serrated Pines
Her 4* Event Weapon.
+Ballistic damage, and +Chaos damage for 5s after using her standard skill.
Very simple, but effective.

These are the only two Chaos-damage Dual SMGs in the game - all other Dual SMGs deal Kinetic damage, however since Bubu has multiple effects that require her to have a Chaos-damage weapon equipped, you really don't want Bubu to be using a non-Chaos damage weapon under any circumstances, so make sure you get Bubu one of her signature weapons.

For weapon parts Bubu wants maximum ATK.

Logistics

Squad

Use Verdure squad - it was specifically designed for her, and is her best logistics squad.

Verdure gives Bubu a simple +25% Chaos damage buff, and +40% ATK buff for 3s after gaining or losing Light Crystals.
If playing properly, this ATK buff is essentially permanent and should have 100% uptime.
Although note that since her uncharged standard skill doesn't give or use Light Crystals, Verdure doesn't help it at all.
Using her uncharged standard skill can thus cause Bubu to lose her Verdure buff as it times out. Using Bubu's uncharged standard skill is thus not recommended.

Stats

For stats, Bubu wants:
Basic: +10.0% ATK
+106 Alignment Index
Special: +8.5% Chaos Damage

The ATK and Chaos damage are obviously useful for just increasing her damage.
Alignment Index gives Bubu more ATK
A max-roll of +106 Alignment Index gives Bubu +5.3% ATK.

Other Stats

Bubu doesn't care for S-Energy, so S-Energy regen is useless to her.
Bubu can't use U-Energy, so U-Energy regen is useless to her, and isn't worth getting to fuel a support operative.
Bubu can't heal herself or create shields.

Bubu's Standard Skill shots all have guaranteed crit, which is where most of her damage comes from, so Crit Rate isn't overly useful for her.
The rest of her damage mostly comes from her ult, which is a skill and thus can't crit at all anyway.
Crit Rate will buff her standard shots, but they are a small part of Bubu's damage, and the extra crit rate doesn't give her that much anyway.
Crit Rate isn't a useless stat - it does buff Bubu's damage, but only by a very tiny amount.

Crit DMG Amplifier is theoretically a good stat, but Bubu's very low base crit dmg value of 30%, combined with the face that much of her rotation is skill damage which can't crit does mean that Crit Dmg Amplifier mods don't actually work out that well for Bubu, and Bubu is better off with Alignment Index rolls instead.
Crit DMG Amplifiier mods are very good for Bubu, but not quite as good as Alignment.

I have added a section to the bottom of this page that goes through some of the maths for why Crit DMG Amplifier mods aren't very good for her.

Manifestation

With M1, Bubu's Chaos damage against enemies with a Fracture Mark ignore 20% of their DEF.
This affects the vast majority of Bubu's damage, and hence is actually a very large increase to her damage.
With M2 and a Chaos weapon equipped, enemies take 20% more ballistic DMG from Bubu.
This is a good increase to her ballistic damage, but only to her ballistic damage.
With M3, for 2s after using her standard skill, Bubu deals 25% more Chaos DMG.
A nice increase that's easy to maintain indefinitely if using her standard damage rotation.
M4 is the standard +1 Standard Skill level, increasing Bubu's damage and Compatibility stats.
As usual for operative M4 buffs, this is just a damage buff of 10%.
It doesn't offer any QoL or anything - it's just more damage.
Bubu gains +20% ATK for 3s after gaining or losing Light Crystals.
Much like her logistics set, this is pretty easy to maintain if using her standard damage rotation.

If you want efficiency (good damage without massive investment) then M3 is a good stopping point, although do note M4 is a better value proposition for Specular Soul than it is for other operatives, although M3 is still the most efficient stopping point if you don't want to get Bubu up to M5.

Good Supports for Bubu - Specular Soul

Specual Soul deals a mix of Ballistic and Skill damage, but mostly ballistic damage, so she ideally wants ballistic buffs.

That she doesn't deal that much skill damage means that operatives that buff skill damage like Siris - Freefin and Marian - Riptide don't work well with Bubu.
Similarly, Bubu doesn't do enough Skill Hits to make Enya - Exuvia and her Zephyr Machine worth it.

Vidya - Celestial Swan for the resistance and DEF shredding
If using Celestial Swan, make sure the other support isn't off element to Bubu.
Fenny - Starshine
Fenny's ballistic damage buffs work well on Bubu.
Bubu's high-capacity magazines and constant skill usage mean that Fenny doesn't need to use her support skill that often either.
Yao - Nightglow
Yao's ATK buff is great for Bubu, her Ballistic buff is good for Bubu, and Bubu crits so much that Yao's crit buffs are also decent for Bubu.
Yao is off-element to Bubu though, so can't be used with Celestial Swan.
Marian - Aquila
Aquila provides very strong generic damage buffs, which makes her an excellent support.
Aquila is off-element to Bubu though (Aquila constantly deals Kinetic damage).
Eatchel - The Cub
A Blitzing Fangs Eatchel provides healing as well as a decent ATK buff.
Not the strongest support these days, but Eatchel's ATK buff is useful for all of Bubu's damage.

Cope supports:

Tess - Phantasia
Bubu's standard damage rotation takes around 16 seconds, during which she will fire 84 shots (possibly more if you aren't gaining a Light Crystal every 16 shots exactly).
This equates to an actual RoF of just 5.25 shots/second.
This is enough that the per-shot bonus from Tess - Phantasia does work out quite well, but not nearly as well as operatives that tend to just keep shooting.
Tess is thus a mediocre off-element choice (Tess adds Frost damage).
Mauxir - Shadow Ka
More damage, and a target that doesn't move.
Shadow Ka is also on-element to Bubu, so you can use Bubu + Shadow Ka + Celestial Swan if you wish.
Shadow Ka isn't the strongest of supports, and Bubu does do a decent amount of non-ballistic damage that Shadow Ka doesn't buff much.
Shadow Ka works, but she just isn't that strong for Bubu.
Marian - Queen of Pain
Marian's chaos damage resistance debuff works very well for Bubu if shooting at an unshielded target.
Since most of Bubu's damage is ballistic, Marian will want her usual setup of Amarna squad and Deep Sea's Call if supporting Bubu.
QoP does work to support Bubu, but QoP is still only a 4*, and is thus weak when compared to the 5* supports.
Fritia - Little Sunshine
A weaker version of Tess. Also off-element (Fritia adds Thermal damage).

Crit DMG Amplifier vs Alignment Index: The Maths
(Also Ballistic:Skill maths)

Note: Again: Contains Maths.

Since Bubu's Standard shots are ballistic, are are where most of her damage comes from, and they always crit, Crit Dmg Amplifier is, theoretically speaking, a good stat for Bubu.

Bubu's Dual SMGs have a 30% CRIT DMG value though, which is very low, and Bubu doesn't gain any extra Crit DMG from anywhere.
Since Crit DMG Amplifier stats only add on to the Crit Dmg value, this means that Crit DMG Amplifier stats aren't actually that good for Bubu, simply due to her low base crit damage value.

Some Maths:

Bubu's regular attacks deal 18.21% of Bubu's ATK as damage (as that's her Dual SMG's Compatibility rating), and have 30% crit damage.
If they crit, they'll be doing 18.21% ATK plus an extra 30% of that, for a total of (18.21% *1.3) = 23.673% ATK damage
With three maxed-roll +10.6% Crit DMG Amplifier mods, Bubu's crits will instead be doing (100% + (30%*(1.106*3)))=39.54% extra damage, so a crit would then be dealing (18.21% * 1.3954) = 25.41% of Bubu's ATK as damage.
Going from 23.673% to 25.41% damage is a paltry 7.3% total increase.
For three maxed-roll logistitcs stats, a 7.3% total damage increase is not good.

For Bubu's standard skill shots, the compatibility rating is much higher (420%) but the maths works out the same, as her Crit Dmg value is the same:

420% base damage per shot
A crit deals (420% * 1.3) = 546% damage
With 3x maxed Crit Dmg Amplifier mods, a crit deals (420% * 1.3954) = 586.068% damage.
Thus, the three Crit Dmg Amplifier mods have added (586.068/546) = 7.33% total damage.

(This is the same maths as doing (new/old) or (1.3954/1.3), but I feel the above might help some people realize what the numbers mean a bit better.)

Bubu's very low Crit Dmg value means that she just doesn't get much value out of Crit DMG Amplifier stats.

Beyond that, there's another problem with them:

Bubu's Standard Rotation and Crit DMG Amplifier

Bubu's rotation is

16 shots from her Dual SMGs, each dealing 18.21%, for each of the 4 Light Crystals.
(18.21% * 16) * 4 = 1,165.44% total damage per rotation.
This is ballistic damage.
4 Spectral Shots from her standard skill, each dealing 420%
(420% * 4) = 1,680% total damage per rotation.
This is ballistic damage.
8 standard skill shots from her ult, each dealing 420%
(252% * 8) = 3,360% total damage per rotation.
This is ballistic damage.
1 Dual Skill Shot from each of the 8 standard skill shots from her ult, each dealing 48% Weapon Compatibility.
(48% * 8) = 384% total damage per rotation.
This is ballistic damage and does technically come from Bubu herself.
The damage from her Specular Slash, dealing 30%, three times, per each of her 8 standard skill shots from her ult.
(30% * 3) * 8 = 720% total damage per rotation (or 1,440% if only hitting one target)
This is skill damage.
The blast from her ult, dealing 1,450% +40% per Fracture Mark
870* + (40% * 24) = 1,450% + 960% = 2,410% total damage per rotation.
This is skill damage.

Doing the maths, this means that Bubu deals:
1,165.44% + 1,680% + 3,360% + 640% = 6,845% Ballistic damage
or 8,549% if you factor in the guaranteed crits.
720% + 2,410% = 3,130% skill damage
meaning that Bubu does around three quarters ballistic damage to one quarter skill damage.

Whilst it's not the highest percentage of skill damage, remembering that skills can't crit means that around a quarter of Bubu's damage gains no benefit from Crit DMG Amplifier mods at all, which makes them even weaker still.

Having three maxed-roll Crit DMG Amplifier mods will give Bubu +7.3% total ballistic damage, which affects around 75% of her damage, for a total dps increase of around 5.5%.
Crit DMG Amplifier mods are ok, but Bubu is a bit better off with the +15.3% ATK she gets from 3x Alignment Index mods.