You could mix a mad bomber/volc demo with any gunslinger armour such as shadowsun and justifier. Then complement the set with trinkets, one for each weapon type.

For example:
Mad bomber helm
Shadowsun
Gun damage trinket
Bomb damage trinket
Swiftstrike buckler

Your fully heated bombs get vh ctr, vh damage
Heated gun gets vh damage, med ctr, high asi.

Alternatively, you could sub out the shield for a stronger one, at the cost of asi for your gun. This is simply a possible combination. It is always possible to substitute the mad bomber for something that protects you better, at the cost of either ctr or damage.

You could also go full chaos, which adds med ctr to both your guns and swords, giving you vh ctr across the board. Then you can add damage trinkets for each weapons, one gun and one bomb.

The bomb damage is not necessary, however, if you plan on only laying down vortex, hazes, and the like. They are not for damage, thus you don't need damage. In such case, a bomb damage trinket can be switched for gun asi/damage/ctr.

For damage bombs, you'll want:
Radiant sun shard. Even if the changes are coming, they are still powerful right now.
Dark retribution, if you have access to the crimson pack and can get it.
Nitronome
The 5* of spike shower, dark briar barrage

Other utility bombs you might want:
Electron vortex, recipes obtained from Krogmo coins
Ash of agni
Venom veiler
Shivermist buster

You also lack guns:
Argent peacemaker/Nova/Storm/Magma/Hail
Polaris in itself is not a good damage weapon. So pick either ap or an alchemer for main damage gun.
A shadow gun, such as sentenza or umbra. Antigua and alchemer line, respectively.
Blitz is a fine weapon, although that damage area is covered by dbb. And dbb is a easier weapon to use against devilites and wolvers. You could still keep blitz for trojans though.

Might want to also invest in an elemental shield. Not a huge priority though, the two shields you do have cover a good amount. For easier floors, a swiftstrike buckler will improve your gunning.

Well Demonicsothe basically told you to get every bomb out there. This is of course the problem with being a bomber: there are quite a few decent bombs out there. If you are going to party most of the time, consider getting vortex bombs. Teammates of all stripes love those, when used well, they can really bump up the damage of the group. Nitro is a great all purpose bomb, especially if you want to carry just one damage bomb that will work everywhere. But you're right: groups hate it. So DBB is a better choice, and since you are going hybrid I would say make a gun one of your shadow weapons. Picking up other status bombs is a good idea, but VT is a very good choice for your first one I think.

I would not do a bomb damage trinket. I think what should come first is CTR. If you are wearing only one piece of bomber armor, no matter what it is, and have no UV's, you will only have CTR Very High. You really really should go for CTR Max!, so get an elite Bomb Focus module to boost that up. Then do whatever you want with the other trinket, as a hybrid a gun trinket is probably a good choice. I'm a mad bomber myself so I'm all about the damage, I'm just saying that CTR should come first before damage. Especially in groups you are going to be dropping bombs like VT and vortex that really aren't damage focused, so the speed with which you can put them down is the most important. Your other option of course is to get UV CTR Med on every bomb you get, then with that plus lvl 10 heat plus one piece of Mad Bomber, you will be at CTR Max. In that case, a damage trinket would be a good idea. I find they make a noticeable difference.

For your bombs, I would first upgrade to Dark Briar Barrage. Then, get a vortex. Electron vortex is my favorite, if you are into the Krogmo thing. Saves money on recipes, for one, plus it's a sweet bomb. But if you really hate the arena, the Graviton vortex isn't all that bad. Next, get another status bomb. If you play a shock level, VT will be worse than useless. So either get Venom Veiler to help out on levels with healers, or Ash of Agni to help kill of creatures faster, or Shivermist. I'd say the choice here really depends on 1) your play style and 2) what levels you play the most. If you're doing a lot of FSC and LoA, Shiver is great. If you're doing a lot of random clockworks crawls, AoA is a good choice. If you are farming arenas and the like, menders are horrible so VV is where you want to go. It's not a bad idea to have them all and switch around depending on the level and your party, but I would get them in the order of priority based on how you like to play.

I love RSS, but it's hard to give advice on that since we're not sure yet what will happen to it. It is only 4*, so it's relatively cheap to get.

I actually use a bomber-gunner loadout pretty often in FSC:

Armors:
Chaos Set (+Med CTR, +Med Damage for all weapons)
2x Elite Trueshot Modules (+VH damage for guns)
Swiftstrike Buckler (+High ASI for all weapons)
[Total bonuses with level 10 gear: Guns CTR VH, Damage Max, ASI High; Bombs CTR VH, Damage Med, ASI High]

Weapons:
Electron Vortex
Neutralizer (I combo this with Vortex for more packed spaces like the bottom right room in FSC - each charge does 500 damage at depth 24 with max damage, and it only goes up from there)
Nova Driver (My staple zombie fighter)
Blitz Needle (Vana/Trojan killer)

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Yes, Chaos has negative STATUS resist, which means that if you catch on fire, for example, you will almost die, but otherwise, it has normal/elemental defense. I offset the status thing with Swiftstrike's high ASI bonus (making myself more offensive and mobile). As a gunner especially, you should strive to never get hit, so pump offense and work your skill when possible. I won't say I never get hit (actually, I play pretty recklessly unless I'm one hit/flame from dying lol) but that's what vitapods, remedy capsules and pills are for.

Now, I use Vortex pretty often for situations with 5+ enemies since it's the best way to capitalize on Neutralizer's charge: When charges tag enemies, they always spawn above the enemy and slowly rotate counter clockwise. If you have monsters all bunched up and want to reliably hit as many as possible at once, you want to tag and immediately detonate charges on the monsters on the right side of the group.

There are two main ways I use Vortex+Neutralizer. I either:
- Tag 4-8 charges on a single enemy then use vortex to pull them in together and detonate them for what will look like a one-shot kill.
- Use Vortex first, use neutralizer charge and detonate, use neutralizer charge and detonate.

The first way takes more setup but feels really satisfying. The second way is more reliable, but doesn't guarantee kills when the bomb explodes. It's best used when you have teammates because the problem with neutralizer is that setting things up take so long, and swordsmen/teammates will tend to kill them before you get to detonate them, so it at least guarantees you contribute lol.

I usually end up finishing them with Nova Driver if they survive anyway.
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Looking back, I really just use the bomb as a support thing.

In all honesty, when I'm facing less than 5 monsters at a time, I'll just use my Driver's normal shots and ricochet the world. I sometimes wonder about whether it's worth doing 3 charges (bomb charge, gun charge, gun charge) or to just use normal attacks the whole time.
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Now, if it were PVP though, I'd go with Justifier and Recon, but... that's another story ;>

@Bella-Donna
Personally I wouldn't waste a trinket slot just to get Damage medium on a bomb. It is true that all damage bonus does help. But to me, if all you're going for is Medium all around, you are going to be, well, mediocre. Better to try and boost one element of the Bombs up a bit. Using Mad Bomber instead of Volcanic Demo would turn that very first loadout you suggested to Bomb Damage VH. It's worth the negative status, especially if you're only wearing one piece of Mad bomber and not the full set (although even then it's worth it).