Last kayak tour: at the end of the day, a dip (without soap) in whatever body of water I had paddled along into the camp. Every other day I'd carry a couple of litres of water a good distance from source, then wash myself quickly with soap there.
Kayak trips are easy, one obviously has water readily available. I don't care if it's sea, lake or creek water, for washing purposes it's all good around here. Bike tours can be more complicated. I'll brush my teeth with the fresh drinking water I have in bottles, but that's about it. I carry wipes, swim when I feel like it and there's a chance, camp by a natural water source / get a proper shower every couple of days at least.
Proper bathing around here requires a sauna, definitely. Guerilla saunas deserve a thread of their own.
--J