How about a lidded
bucket with a damp towel in the bottom? I put damp towels in the bottom of my produce drawers in the fridge to keep things fresh without needing to wrap, and it works well in that setting. On a hot day things are going to wilt no matter what, though.
For
poop bags, there are bioplastics. The last ones I bought were from a company called Earth Rated. They have two kinds, one plastic and one starch based. The bags last me a long time, so I don't remember what I bought before that, but i'm fairly sure it was another company with a veg-based bag as well. There are also those liners for the kitchen
compost bucket that are starch. Never used them, so I don't know anything about strength, available sizes, etc.