>> The problem will be how to collect gray water from the bottom. The
national parks I camped do not allow discharging gray water right on the
spot. How do you volks do on this? <<

I have a grey water collecting "tray" type thing made of rubber that goes at
the bottom of the shower. It has a drain that connects to a hose.

To be quite honest, I have it for show only for when the rangers show up.
It is big bulky and hard to manage. Once it's filled with water and you
start to pick it up to drain into the drain plug it becomes a big wet mess.
Remember, you're inside the shower trying to do this.  Very impractical.  I
wait until there are no rangers in sight and just dump the water out into
the poison ivy which is the required campground foliage in state parks.

Bryan