A bow will not fire (or load up) when it is used in the offhand slot. I put a bow in the offhand slot, and either something with no right-click effect or nothing at all in my selected hotbar slot. I expected the bow to load up and fire when I right clicked, but all the game tried to do was right click with my selected item in my hotbar. You could recreate this by putting a bow in the offhand slot, and right clicking as to fire it from the offhand slot.