I shouldn't be answering considering I'm positively addicted to 1. riding in bike clothes, 2. taking a hot shower and putting on clean clothes once I get to work...

But - i'm even more addicted to bike commuting. It really is the best way EVER to get to work. Hands down. I've tried them all. Just bus is relaxing and all that, but I get to work still sleepy and groggy, and get home still moping about work stuff. Riding a bike puts me in an instant (well, almost instant) good and energetic mood for the next part of the day. You really really have to give a proper try. Just don't try to do it all in the first week, it'll feel like a hassle.

Anyway - if I didn't have a shower at work I'd try to cool off for ten minutes, then head for the bathroom with a washcloth. You can wash your whole body and really get quite clean with a washcloth wrung out in hot water and a little soap. Edit: I see you're taking a bus or train in between, that will take care of the cooling down. But I'd definitely bring a dry top, a warm fleece and maybe socks and change immediately after parking my bike, I tend to get worked up and sweaty no matter the weather, then very cold right after.