Try your local Frame Shop (maybe even Joann's) Sometimes they will give you the scraps from mat board and foam board. I have an unending supply, my daughter is a professional framer.
I take the mat board and glue a couple of pieces together for a more firm bottom. Make a cover case with lining fabric so it just slips out for washing.

Great idea

I just wonder if it would bend under weight? Anyone have this issue?

I cruise the Clearance Aisle at WalMart for placemats on clearance and buy several. They are big enough for purse bottoms and take up very little room under fabric on the shelf.

Placemats, what a wonderful idea.

Which one? I know the double mat board & foam core does not bend.

I have used cardboard, foam core board, plastic canvas and leftover floor tiles. I like the floor tiles the best can get 2 out of a 12 inch tile.

I use a heavy mat board. I cover it with fabric and it works really well. I get it in the art department at Hobby Lobby, but you can find it at most craft shops or art supply stores. I am curious now about the "plastic cardboard" you mentioned, and will definitely check it out. If it is the same thing that davidwent mentioned, it should be strong enough to hold up for lot's of use.

Great tip!

My solution to the bag bottoms was to go to my local lumber yard. They get into their scrap bin and get me all the plexiglass I want and for 50 cents each they will cut it to size. They like getting rid of their scraps. When I go I generally have them cut several of the standard sizes. Sure works for me.