Freud, dude, a lot of people here either...

1. Pack their work cloths in a separate bag.
2. Leave a set (or a whole week or more) of work cloths at work for the days to commute in.

But it seems most people wear other cloths to bike in to work so they don't have to sit around in sweaty cloths for very long.

Button down shirts ... there are plenty of wrinkle free options out there as well as tricks like rolling the cloths to help limit the wrinkles.

In any event it's time to stop wearing your work cloths to bike in.

When I was starting a learning to run program over at calorie-count.com the first few weeks I ran in my work cloths. Temps were better then and I wasn't sweating enough to matter. Now I'm in week 6 and I wouldn't think of doing that and instead bring workout cloths and dedorant to work.