I believe a bane bow firing an arrow and a bow firing a bane arrow are equivalent. In either case, the arrow ends up with the bane property. I do not consider a +1 bane bow's enhancement bonus to be +3; it is a +1 bow with the bane property. As soon as it is fired at an appropriate opponent, it receives an effective increase (or a bonus to its bonus, however you want to look at it). Bows and arrows have a method for determining their bonus, and bane increases the "normal" bonus. A +1 arrow fired from a +5 bow is normally treated as +5.
The case of the bane, bane longsword is an interesting... can a weapon be enchanted more than once with the bane property? It seems to me that bane is a property, and you choose which kind of bane. Allowing more than one version of bane seems okay, but I don't see that it's allowed. As nearly as I can tell, bow and arrow is the only way to get bane (chaotic outsider) and bane (evil outsider) on the same weapon.
It is interesting to ponder whether a bane weapon can benefit from Greater Magic Weapon... is a +1 longsword affected by a +3 GMP "normally" a +1 weapon or a +3 one?