Here is how we take a shower in our trailer. The set up take no more than 10 minutes and the 4 1/2 gal. bucket full to 3 inches to the top of warm water will be enough for 2 showers.
The upper part is made from plastic plumbing pipes and connecting pieces. Only the ring parts and the shower parts are glued together. But the shower assembly is not glued to the ring. The bottom part is a 60 gal water heater pan. 2 shower curtains are attached to the top part and fall
nicely into the bottom pan. The shower pump is made by Coleman and the bottom pump is a small and not expensive bilge pump easy to find in a marine store. I made a hole in the floor of the trailer to evacuate the water where possible. The bilge pump will rise the water into the sink if needed to hold it into the gray water tank. After usage, everything is disassembled and store inside the water pan and under the permanent bed.
We used this set up many times during the last 5 years specially when we go to florida. It is quite usefull.
I posted about this a few years ago but it got lost.
The shower pump is from the Coleman battery-power shower, maybe not available any more.
The bilge pump is the Attwood V500, around 20$