The usual method is to use a larger (often cotton) bag. A large pillow case might work. Often the quilt vendor either provides that storage bag or has it as an optional purchase, usually about $10 USD. REI sells a nylon storage bag that allows breathability because one side is wide mesh. These are stored in dry places, away from pets. Mine are in a closet, top shelf.
I don't mind if the bag is squished a little bit. The goal is to allow it to loft as much as possible - not have it mashed down most of its life in a compression bag.