If I have wet clothes in the morning, I usually strap them down on top of a front pannier, the Ortlieb Frontroller has a strap that goes over the top that I use. I think I get better air flow up front and less dust up front than I would if I put them on back. But I almost never get dry clothes by the end of the day that way, I mostly leave them outside so that they don't get stale inside a waterproof pannier. On some trips I carried a small mesh bag to put damp clothes in for strapping down on top of a pannier.

Agree with DJB, start early, quit early when you still have daylight to start drying stuff out.

Instead of washing in the shower, I bring a flat drain stopper so I can use soap and do laundry in the sink. The photos above where I had my clothesline tied to my yellow bike, that line is about 25 feet long and has about two dozen metal wire clothespins on it.