Advice from Dave Zabriskie via Bicycling Magazine:

Dave Zabriskie, 6-Time U.S. National Time-Trial Champion and 2-Time Tour de France Stage Winner
"Frank McCormack showed me how to dry my clothes. He laid out a dry towel, then he laid the wet clothes on the towel after he washed them. He rolled the towel up, then stepped on it, and finally wrung it as hard as he could. After that, you have to hang your clothes for only a little bit before they're dry."