The description of Bane as a magical quality of a weapon specifically points out bows, crossbows, and slings as being bestowed upon their ammo.
Can a firearm have this magical quality on it?
If Bane is granted on a firearm's ammo, what would be the cost of upgrading the basic weapon to the +1 enchantment of Bane- using Pathfinder Society rules?
For the purposes of Maximum Item cost of the above upgrade, a character with 16 fame has a purchase limit of 3,000 gp. Is the above item cost figured at what is paid for it, or is it figured out as what the item is worth on the market (full gp value if it were to be purchased straight up)?
All magic enhancements and enchantments that CAN be cast on a ranged weapon apply their effects to the ammo when the weapon is fired. This applies to firearms as well. So yes, you can have a Bane firearm. Don't forget that the weapon must ALSO have at least +1 enhancement on it too, so you're really talking about at +1 Bane firearm.
The cost of that is priced as if it were a +2 weapon (+1 for the enhancement and +1 for Bane). By Core, this means it's 8,000gp + 300 for Masterwork cost + the cost of the firearm.
I don't play PFS so I don't know how the purchase rules apply, but it sounds like that is quite a bit over your limit.
On a side note, are you sure you want a Bane weapon for PFS? Every time you show up at a game store or convention or wherever you go, you get a new GM and a new adventure and it might not have ANY of the specific creature type that your gun is good against. For example, if you make it Bane vs. Undead and then your next 5 adventures have NO undead in them, then you've wasted a bunch of money for no benefit.