I was thinking of putting a bed in my basement...There is an exit to the side door up the stairs to the outside plus I have a basement door that leads to the garage and outside.
Well first of all for safety reasons you seem covered. You have exits in two directions and possibly three if the regular windows can fit a human.
From a code aspect there is nothing that says you cannot put a bed in your basement. Now there are real estate listing rules that do not count a living space as a bedroom in a basement unless it meets certain criteria.
For most home listings there must be a door that you can walk out of in the basement for a room to be considered a bedroom in a basement. You seem to have that in the door to the garage. Also allowable is an egress window.
That being said you can put a bed where ever you want and there are no laws against that.
Sleeping rooms shall have an egress window or a door that opens directly to the outside. (See ICC R302.6.) The door cannot be in a hallway or open into the house or garage.
Garages are to be separated from single family residences by 1/2” gypsum board on garage side ONLY, and the garage cannot open into a sleeping room. (See ICC Table R302.6.)
The door between the garage and house shall be a solid wood door a minimum of 1 3/8” thick and is NOT permitted into a sleeping room. (See ICC R302.5.1.1.)