Packtowls are a common backpacking item and available at multiple locations. Examples are
REI or
Campmor. They must be used to be believed. You can wash and wring them out, then use immediately. Being synthetic they dry very rapidly. They contain a handy snap loop and can be dried around the shower head, shower vent or on an awning bar. I'd recommend nothing more or less than the 20" x 45" size. Two of them hold me for a very long time -- one for hair/face and a second for body. I've posted about them at least twice before. Good reminder, Antique Pedaler!