Here in Oregon, single use plastic bags have gone the way of the beta. I am glad. I had a particularly soggy shopping trip today, and I came upon a trick that you might want to modify. I happened to have a wicker basket that I got and it was perfect for up-ending the wet bag and letting it drain.
So the chances are pretty slim that you will have the perfect basket. So I would measure your average bag, and perhaps find a crate or plastic box, old waste basket (my personal favorite), or even that wrapping paper container we all love.
Anything that would let your bags drip dry for sanitation and durability would work. Hope you like this. PBP
Source: My wet bag