The Pathfinder Alchemist sections describes it pretty thoroughly, you mix up a bunch of 'catalyst' vials. Those vials are then used to mix and throw the bomb within the same round.
You can have any number of catalyst vials you want, generally at least equal to the number of bombs you can throw, but you could have hundreds if you want. However, you can only mix and throw your allotted bombs per day.
The rules aren't particularly clear when that number resets, so you should probably work that out with your GM. Midnight, 6am, whatever.
Bombs are like most other class abilities all mimic a spell casters regaining spells. Clerics are the exception in that in later publications clerics have to pick a set time to regain their spells after the required rest. Eight hours rest then an hour of meditation, memorization or what not and then a character has his spells or whatever returned to him.
The only way to get more bombs per day is take the feat extra bombs and or take a race that gains more bombs per day as a favored class feature.
Another suggestion is carry a ranged weapon to supplement the bombs. Not all encounters or monsters require bombs to deal with.
You shouldn't think of bombs as an attack. At least if you aren't facing a one big monster like a dragon (in which case- nova like hell, since it is vulnerable to that and has enough going on that it can wreck your potion making rear).
You add abilities onto the bomb via discoveries. This basically makes them into spells- but slightly better than most spells, since the DCs scale with level.
And you can pick any 'spell' at will when you 'cast' (throw) it. So like a sorcerer, but hyper focused since you only have your discoveries as 'spells known'. These discoveries do things like debuff (like confusion bomb), battlefield control (such asn entangling bomb), or other useful things (such as the dispel bomb, which sacrifices damage to do a dispel).
So at times, just a single bomb can decide an entire fight. Just throwing all 10 out as nova damage is not the best move. Good to have the option, of course, since again- DRAGONS- but you can do better things. So it is best to do a combo of throwing a bomb to alter the entire fight, and then use extracts to buff/debuff/various things like spit swarms. Also, you can always have alchemical weapons to do something useful when you can't do either of those (since you get int to damage, and you can do well enough with your usual int/dex build)