Generally on tour, the clothing that's against my skin is light fiber that I can wash out myself and will dry overnight. YMMV
The sink sort of works but the pad on mine doesn't dry overnight. Sometimes, I just go into the shower with kit on and do it all at once. I strap the spare bibs to the rear rack or bag, pad facing the Sun to completely dry. I've also worn the same bibs for around 800 miles several times, so, that is an option too. But, I was more thinking that I could spend $50-100 ever couple of days to have someone else properly clean my stuff.
Beyond cycling clothing, I got the impression OP wanted to stay in decent hotels and have a nice meal at night where grubby cycling kit would not fit. A merino polo and light slacks should stay clean on a shorter tour.