According to the statblock, unlimited. A reasonable limitation would be 12/day (for 12 HD and no Int modifier).
Unlimited.
And changing that would be akin to taking away the spell immunity of an iron golem that a PC created because... reasons, mumble mumble.
It's a golem, you made it. Golem crafting is a PC option that most players don't bother with; limiting this feature makes this golem not worth the money invested in it.
From the statblock entry, it is unlimited.
That doesn't mean the GM has to allow it for a PC's golem. Making both (daily uses, total uses) these unlimited make this very powerful and basically creates another PC in the party, and this thing isn't really that expensive to make for what you are getting for it.
Also, since the ability isn't (Su), like an alchemist's bombs are, you could argue that the alchemical materials runs out at some point, requiring refilling (like an iron cobra requires new doses of poison).
If I were concerned about it as a GM, I would let the player choose between an appropriate daily limit (12/day seems reasonable; so does the class level + Int mod of the alchemist at the golem's creation), or a max # of potions before it runs out and needs to be "recharged" (120 bombs total & it takes 1000gp worth of potions to 'recharge' it). This gives the players the option at least.
I wouldn't change much of anything though except possibly the encounter toughness due to basically having another party member that isn't splitting party resources.
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Bombs (Ex) As a standard action, an alchemical golem can throw a bomb as a ranged touch attack to a distance of 60 feet (no range increment). If the attack misses, treat it as a thrown splash weapon to determine where it lands. Anyone struck by an alchemical golem's bomb takes 8d6 points of acid, cold, electricity, or fire damage (determine type randomly). All creatures adjacent to the location where the bomb hits take 1d6 points of energy damage of the same type.
Unlimited number of use s of the bomb ability.
As the energy type is random (I suppose with each use of the ability) it isn't so impressive.It cost 3 feats and about 1/4 of a level 10 character WBL (crafting cost).
Also adding to its unimpressive-ness is that it does not have the typical alchemist bomber feats of point-blank shot, precise shot, and the one that lets you exclude squares.
Also, this is a golem and not your familiar, and so giving it specific instructions isn't going to work well. Between that and the -8 penalty you will typically have throwing into melee, your party may be more annoyed than the GM.
Here are some things that would help me as the GM get over the initial sticker shock:
- No feats typical of a throwing build, -4 to -8 penalty will be common
- Additionally will be damaging own party somewhat frequently
- Cannot give it detailed commands/instruction (actually, your ability to command it at all seems to be within the purview of the GM, apart from being able to activate/disactivate it)
- Harder to heal
- Time consuming to rebuild when destroyed