If I'm using a bound bow and I switch to a spell, will the bow disappear? If not, is there a way to hotkey it? Would be extremely tedious having to enter the inventory every time to reequip it after casting a spell.

Sheathing = dispell.

When you sheathe a weapon you dispel. When you switch the bound bow it will disapear making you recast it again. In order to hotkey spells you will have to add them to favorites and than highlight the item in favorites and pressing the respective button.

Damn... well that makes bound weapons completely useless for my character then.