I fell and abraded the top of my hand. About a 2by2 area. I am using bactricin on it daily. Should I just let it air dry?

Yes if superficial. Good to let air get to it if superficial. Might need to be covered by tegaderm if you are handling food.
Moisture. Keeping the wound moist with antibiotic ointment will help it heal faster and prevent infection. Crust attracts bacteria.
Treatment- abrasion. I recommend aquphor ointment, available over the counter. It has a lower risk of allergic reaction than bacitracin.