I have a speedy and when I know that I'm going to be shopping or doing something all day, I bring my strap with me. By bringing the strap with me I can have it hang cross body while I'm washing my hands. As far as in the stall goes, or if I don't have my strap with me and I'm at the sink, I will take a wad of paper towels and put the speedy on top of that. It's not ideal, but it's better than letting the canvas touch whatever surface you don't want it to touch. I do the same thing at restaurants on the chair next to me on in the booth.
I do the same. I always attach a strap to my speedy's when carrying because it is so funtional. With the strap, it removes the worries about germs or dirt and reduce the possiblity of theft.