Teach your dog to ride inside of a crate, and cover the crate with large towels or sheets to block your dog's view. (dogtrainingnation.com)
There were always plenty of larger towels to bath / shower and plenty of towels to use as floor mats in the bathroom / sink areas. (havebabywilltravel.com)
Also, I have old large towels reserved for floor use only (I have a thing against mixing hand and floor towels). (diaperpincorner.com)