That's a GREAT idea!!

I just cut up plastic milk jugs to the size I need.

after the last election season I picked up several politician's signs left behind and planned to throw them away, but now realize that the corrogated plastic is PERFECT for the bottom of bags. It's lightweight and sturdy. Visit your local sign shop to get a supply. Easy to cut with a box cutter.

I have used old cutting mats cut to size!

I use the corrogated plastic, easy to clean and to cut

I use the needlepoint plastic they have at Joanns.

Depending on how stiff you want it...

I need to replace the once-stiff cardboard in a Vera Bradley bag. I'd read somewhere that someone used those stick-on vinyl tiles cut to size to provide a base for a bag. I've seen them sold individually at Home Depot or Lowes.

I go to my local sign shop. They have a barrel of scrap sign material that is very stiff. If they only have thinner stuff, I use double stick tape to stick 2 pcs together. I always cover the hard base with fabric, so sticking 2 pcs together isn't a problem. The prices on the pieces vary, but I usually can get a bunch of stuff for under $5.

I use the cheap plastic cutting mats from the dollar store. They are usually sold in sets of 3 and are about the size of a place mat. The vinyl placemats will work as well.

I make a sleave and recycle cardboard. I love the idea of the plastic canvas but am trying to be frugal these days and make every peeny count ;)