Did you try un-equipping the bow/weapon first, then equipping a new one? How about selling the one you have directly from the equipped list of inventory?
Does it work any better selecting a weapon in the inventory, hitting A and then Equip?
Did you re-assign the buttons to something else, try it, and then switch back?
Do you have any previous saves (preferable recent) that are working properly? It might help to exit out to the dashboard and restart the game again (worth trying, anyway).
