I wear cycling shorts and a cotton t-shirt (hopefully I can get an actual cycling jersey ). The t-shirt gets soaked on the ride, but I just drape it over the back of my chair, turn it over around lunch, and it's dry by the time I get ready to leave work. Same with the shorts, only they get drape over the waste can under my desk (no need to shock everyone ).

The only issue I have with drying my clothes is when I wash them after I get home, mostly the time it takes. I hand wash the shirt and shorts then hang them on a wooden drying rack in the bathtub. Takes about 24 hours or so to dry (a fan blowing on the clothes helps speed things up).