There are all kinds of spray bottles for cleaners, pick a large economy bottle and after you use the cleaner don't throw the bottle away. I've used Windex bottles because they have a fine spray, some have adjustable sprays from fine mist to a stream. Heat some water, fill the bottle. Wet the wash cloth and soap it up, spray the body in sections, wash it, spray rinse. Wipe off with another dry cloth, stand on a towel or set in a seat and dry as you go, head, arms, trunk/back, tail end legs and feet, you'll figure it out.
It takes very little water to clean the body, it's a "spit bath" :wings:
Wasting a gallon of water for one bathing session once a day on a five day trip for two is 10 gallons of water. I'll only carry 20 gallons, so using half to bathe and let it go to the ground isn't real efficient usage. Gray water can wash other things too. :snorkel: