Wool jerseys, bring 3 pair cycling shorts, wash each pair of shorts after each wearing. Shorts get washed in the sink or shower and hung to dry, and once or twice a week (depending on what's ahead of me) I find a laundromat and put everything in a machine. 3 pair of shorts means I can go a few days without washing them if I have to, or a pair can take an extra day to dry. For off the bike clothing, I try to use synthetics that will dry in a hurry, or wool T-shirts that can go a while without washing.
Most European campgrounds and hostels have some kind of laundry facilities, but they tend to cost a fortune.