Well, on p.550 it says the "stat block includes the price and features for a single dose." So in order to achieve the effects listed, the target must have been subjected to one dose of poison. There is nothing saying that having less than a dose applied has any effect whatsoever.
So, one dose per weapon/arrow/bolt.
For melee weapons, if you miss the blade remains poisoned. However, it's not entirely clear what happens to a poisoned arrow if it misses. Afaik, there are currently no rules regarding reusing (non-magical) ammo, but since ammo is listed under "consumables" in chapter 11, I'd say it's spent even if it misses.
It potentially makes ranged poison use more expensive, but then, being at range also makes it less dangerous to the user, so balanced (and not different from regular ranged attacks which need to use limited arrows, while melee can just go on forever).
Minor point, a real stickler of a gm might not allow you to poison arrows/bolts since those aren't weapons, they are ammo. And the rules under poisons talks about poisoning weapons (page 550) in regards to injury poison.
But if they pull that you can always say you are poisoning the crossbow/bow and by the rules, that seems to work.