Bumper stickers shouldn't need to be anything special by thickness. Just print, lam if you want and get it gone. Heck, this is something that even with shop minimums should almost be not worth it in small runs and can get a screen printed sticker (even die cut) on vinyl in large runs for the same cost as you doing all the work for a small run and all you do is send the file off and open the box and hand off the final product when it comes in.
don't waste your time looking for special stuff on jobs like this ... in the end it's not worth it unless they want to pay a premium for stuff they don't need. (like the whole roll of vinyl you'll need to order that you will never need save for that one job).