Using a bow, if you switch to another item at the exact moment the arrow leaves the bow, that item will become a bow and include enchantments. My enchanted sword went missing which raised my suspicion. I've turned a stone sword, golden sword, wooden sword, wooden shovel, and a stack of netherack into the bow used, retaining the same enchantments and durability. The stack of netherack becomes just one bow, not a stack of 64 bows. All of the bows will go on the floor to despawn, but I miss my maxed out sword.

I am playing as a joined player in a multiplayer world.

I just tested in a brand new creative world and turned a diamond sword into a bow, as the host.