The larger service stations ... and especially the truck stops ... often have the showers for the truckers. Those ones are usually located right on the edge of city, or a little way out of a city, sometimes even halfway between two cities ... and usually on major highways, trucking routes.

You probably don't want to do most of your tour on major highways, but if you happen to be on one and happen to encounter a large service station in the middle of nowhere, there's a chance it might have a shower.