I thought of using a storage bin and didn't consider using it as a double duty container.
I did find this doing a Google search:
I actually think I can make one of these to fit my shower tent. I have a ton of vinyl from an old billboard that is heavy enough to fabricate this and still flexible enough that I can roll it up for storage.
I was thinking of taking a 12V pump and just pumping the water into my grey water jug.
I'll have to take some measurements to see if this is feasible.