I'm looking for help with building a bomb-slinging alchemist at level 10. Assume 25 point buy for initial generation. The focus is getting the most effective bomb usage possible. Fast bombs is clearly desired the moment it becomes a legal choice allowing for multiple attacks due to BAB progression, rapid shot feat, and possibly other options. Source options are Core, Advanced Players Guide, Ultimate Magic, and Ultimate Combat. Which class-related options should I be considering? I do not need a complete character build.
It's important to note that (with Fast Bombs) you can throw bombs with both hands if you get the Two Weapon Fighting feats, and this stacks with Rapid Shot. This lets a 10th level alchemist throw five bombs a round at +3/+3/+3/-2/-2 (before adding Dex or point-blank). Not very high, but you don't need that high a bonus. Personally I'd go this route before going for Rapid Shot, simply because you can continue gaining more attacks as you spend more feats.
You're also likely to want dispelling bombs for the sheer utility.
I have a player who is doing just this kind of build, so I think I can help you a little.
You don't have a lot of options when related to combat feats. The following you should consider your main focus:
(Important to note, Deadly Aim does not work with bombs)
Arguably, Alchemists are a 1 attribute class. This is Intelligence. Your bombs per day and additional bomb damage are based off of this. Bump it fairly high at the beginning and then put a little into Dex, so you can reliably hit Touch AC and a little into Con, so you're not super-squishy.
You'll be aiming for Touch AC most of the time, so you don't need to worry too much about whether or not you're going to hit them. Plus if they have a touch AC which is too high to hit, you can simply target a grid intersection (AC 5) and just do splash damage to your foes.
Additionally, get some means of Flight, so that you can drop bombs on your enemies from above, and laugh when they only have melee weapons.