I'm not suggesting anyone spend $400 for a shower, but the Evershower is in some ways intriguing. (Link:
https://evershower.com/#FAQ). The FAQ verifies, yes, the pump recirculates your dirty shower water until you're ready for a fresh rinse (or not-yuck). The part I like is being able to enjoy the flow for as long as you want (or the water is a good temp).
My shower consists of a shower head attached to a 12 volt marine bilge pump, a collapsible bucket and a folding dog pool. I have rarely used it. the pool is too big, really. I always carry an empty plastic tote nested outside a full one, and sometimes wash my hair over that.
A 2.5 gallon solar shower has been added to the water works, but I haven't needed it yet.
Before that, I had a couple (they break) of 12 volt drop-in-the-bucket camping showers. If needed, I could pump the gray water out of my shower pan (a masonry tub). To keeping any stray hair out of the pump, I put a knee high stocking over the inlet. A marine sponge is good for that last bit. Usually, I could just pour the water into a jug manually.
Before that, I used a garden sprayer. It worked and is also nice for washing dishes, but required too much room and maintenance (just Vaseline on the seals, but I'm lazy).
Returning to the Evershower concept, I would like to try using my pump/shower head in that way, recirculating a small amount of water until I'm ready to rinse. Not sure how deep the water would need to be for my pump.
As for sitting down to shower? After spending a day at a Korean-themed bathhouse, I had to seriously question why we work to defy gravity and risk life and limb to shower. Any clues? Sitting on a small stool works pretty well--especially in a regular roof van.