The mattress doesn't have to be slid into a single bag. It just has to be wrapped or enveloped in plastic.
Take a whole bunch of black trash barrel bags (readily available in any grocery).
Cut the bags open to increase their coverage area. Tape several together with duct tape or masking tape. So a few open ones taped together sturdily makes a "sheet" of plastic.
Put a few of those "sheets" together and lay the mattress on top of those. Now cover the top surface of the mattress with another "sheet" of plastic bags taped together. Overlap the edges, top and bottom, and tape closed. Mattress will be covered as required .
The bigger the mattress, the more trash bags you need, so buy a couple of packages of trash can bags. Dry cleaning bags can be used in lieu of trash bags.
This ain't rocket science. Bunch of bags taped together to cover a mattress. Hard to do alone, better with two people.