When I use clay I always leave it open. I normally just spread the clay over the area
When I use clay I always put the clay, than paper towl that is a bit wet, than the bandages. For me it is the best way to go ! Keeps the legs cool and clean
You can leave it in the open air. You can also use a brown paper type wrap that is wet and wrap that over the clay. Once you do that, you can wrap with cottons and bandages. For the brown paper, you can use meat wrapping paper or larger brown lunch bags. I'm not sure where you live, so I'm not sure what else you might be able to use.
In my experience, everyone I know uses bandages. To keep the mud from sticking to the wraps and pulling out hair, my mom used to use plastic wrap, but only for short periods of time.