You might like a 3/4 BAB class with tricks that work the action economy for you - inquisitors or warpriests have swift action buffs, or an eldritch archer magus can do some fun stuff on a full attack with spell combat. 7-8 levels in one of those gets you 3rd level spells which while not up to any half-serious spellcaster does get you some fun effects. Look up shield of darkness or channel vigor or storm step.
There's also the option of taking a one-level dip in a class which can boost dexterity - alchemist, urban bloodrager, savage technologist barbarian or whatever - or even more if you like that particular class.
I like (Bolt Ace) Gunslinger 1/(Grenadier) Alchemist X.
Grab yourself a Heavy Crossbow for that 120' range increment (which can be Touch AC for a Bolt Ace), Take the EXPLOSIVE MISSILE discovery and you can fire 1 explosive bolt per round.
Upgrade to a CONDUCTIVE crossbow when you find you have more bombs/day than you can use, and if you want you can upgrade to a DISTANCE crossbow if 120' vs touch AC doesn't seem long enough (or if you really have to shoot something 2400 feet away).
Of course if you want to do more with the actual crossbow damage then Bolt Ace 5 is better (and probably Eldritch Archer Magus is better than Alchemist).
So to be honest using Explosive Missile every round would probably be less damage than just full-attacking with either your crossbow or your bombs at high level, but it is cool.
If you wanted to go Bolt Ace 5/Alchemist X, you could still make use of a conductive weapon for the best of both worlds. Full attack with your crossbow, and one hit per round also explodes with your bomb damage. Because of the way Conductive Weapon is worded, you don't have to decide to use the bomb until the hit is confirmed, so you never waste those bombs. I haven't checked this, but the wording also makes me think the bombs can't crit (It's probably worth checking these in the forums and FAQ's before you play, and more importantly with your GM).
At 6th level the grenadier can also attach an alchemical item (tanglefoot bag anyone?) once per round as a swift action.
So if you went Bolt Ace 5/Alchemist 8, you'd have +11 BAB, you should have 8+INT bombs per day.
I'd go something like: (Light Crossbow) 1. Point Blank Shot, 3. Precise Shot, 4. Rapid Reload, 5. Rapid Shot, 7. Weapon Focus, 9. Snap Shot, 11. Improved Critical, 13. Improved Snap Shot.
For alchemist discoveries you've got: DARKNESS BOMB (seems useful for someone with light blindness), VOID BOMB and maybe BLACKSTAR BOMB. If you're willing to spend your level 13 feat on an alchemist discovery you could also get ALCHEMICAL ZOMBIE and BONESHARD BOMB. There's a bunch more, but those are the ones I thought suited an evil drown noble. It is worth noting that the DC's for bombs is 10 + (1/2 your Alchemist level) + INT, which will be 14 + INT at Bolt Ace 5/Alchemist 8.
You'd also have 3rd level Extracts, so you could fly/haste/etc.
This ended up being more viable than I thought, I hope that was helpful =)
The description for bombs (simplified) says that only the initial 1d6 is multiplied on a crit. So bombs do crit, it's just not very much. Conductive should stack with Explosive Missle, making a single attack for the round but doing two bombs (at the cost of three uses) worth of damage + any other enchantments the ammo has + base damage from the ammo itself on a successful hit.
Conductive will stack with Explosive Missile, so you're right about that. And while the bomb damage doesn't get much from a crit ({4d6 + INT} becomes {5d6 + (2 X INT)}) it does a lot for the crossbow damage (At 5th level Bolt Ace gets X3 crits). Having a 17-20/X3 crit-range on 5 attacks per round (+10/+10/+10/+5/+0 including rapid shot and haste) is pretty great.
The reason I'm not recommending Explosive Missile more highly is that a level 13 Bolt Ace would do more damage on a full attack than a Bolt Ace/Alchemist using Explosive Missile, or a level 13 Alchemist could do more damage full-attacking with the Fast Bombs discovery. Going Bolt Ace 5/Alchemist X gives you dex to damage and higher crit range with your crossbow, and then going Alchemist and getting yourself a conductive crossbow will let you use one alchemist bomb per round on top of all those attacks (at the cost of 2 bombs per use). Snap Shot and Improved Snap Shot are just for fun.
As for the discoveries, take what you like. I just took a look and those ones sounded thematic, but they weren't the strongest options.
If you DO want to go with Explosive Missile (it is super cool) then I'd go full-alchemist. I'd also take the BULLSEYE SHOT feat at level 7. You only get 1 attack per round, so you really don't want to miss.
Another vote for bolt ace 5 and inquisitor. Grab a nice large Xbow and go for the vital strike route.
There was more than one thread here about how to do 12d6+a lot with a move each rund. Without buffs.