Full disclosure: We only get six or eight inches a year of rain around here, so spray isn't much of a problem. But when we go over the mountain to California, I just cover the Brooks saddle with a plastic bag. When we get where we're going, I put the bike in the motel shower, rinse it off and lube.
If I use the rooftop carrier instead of the hitch rack, just wiping is usually sufficient. Bikes are pretty well sealed, and I never find evidence of water inside when I tear things down.
Motel owners hate every aspect of this, by the way.