When I travel by bike, no matter how many days (or weeks) I'm gone, I carry two pair of riding underwear, 2 pair of riding socks, 2 wicking shirts. Maybe a pair of shorts, or long pants - depending on expected weather conditions.
You can easily wash your socks/underwear/shirts in the hotel sink. I could probably get by with one of each, since I wash nightly; takes about 15 minutes:
1. Fill Hotel bathroom sink with warm water (1/2 to 3/4 full).
2. Squeeze in the Tide travel pack (pictured below; you can find in Grocery Store "Travel Size" section).
3. Hand Wash garments, and then let them soak for 10 minutes.
4. Rinse thoroughly.
5. Lay large hotel bath towel on bed, and arrange washed garments on it. Roll it up, so garments are inside.
6. Place rolled towel on floor, and step all over it to wring out the clothes.
7. Hang clothes, and they're dry by morning.
The clothes can be tumble dried, but I prefer hanging.... Much easier than wasting time doing somersaults all around the room....