As long as it is set up on a flat and immobile surface just like it would be while in use, you can store your bed frame assembled with your mattress on top of it. Ensure to wrap your bed frame separately from your mattress.
If you don’t have the space to store your bed frame set-up, you’ll need to disassemble it and wrap the pieces in plastic to protect them from moisture, just as you would with your mattress. Wooden and iron bed frames are also vulnerable to humidity, so it’s essential to protect them from moisture.