I am about to start a tour on my Brompton folding bike with the Brompton bag on the front and standard hiking backpack rigged to the rear with bungee cords. This setup works except that I don't have a rain cover for the backpack. I was going to use trash bags but that will get expensive and seems wasteful, and I can't justify spending $30 on a simple rain cover.

Any suggestions for waterproofing my bag when necessary?

[And since someone will ask ... I almost bought a used set of Ortlieb front panniers which would have fit on my rear rack, but the backpack works better because I can wear it when my bike is folded.]