So if I bring my own water, which would be easy enough to do, collect the runoff, slightly harder and dispose of it properly. It might be possibly somewhat legal. The feds and there rules are killing me. I think they need to install showers at all the main campgrounds.
Ya know, I can understand these rules.

Soapy nasty bath water on the ground will attract critters and bees, etc. Someone would take a shower after breaking camp and the next person that rolled into the camp would find a muddy mess of soapy water - then people would start cleaning pots and pans and dishes and there would be coffee grounds everywhere, etc.

I still think just a simple shower setup would be A-Ok and could generate some additional revenue for NPS or Forever resorts. It doesn't have to be in the basin per say, just down in a more central location like PJ. Coin operated showers, limit water use by military showers, etc. Heck, make it a luke warm shower at that.
Or, you could get a Starcraft pop-up camper like I have that has a toidy and a shower and also has black/gray water containment.