I have a short bike commute, 1.72 miles to the train. I can usually get by, even in the summer without changing or bathing. Even so, I have a shower & locker at work, so I can't help you directly.

Lots of folks who don't have a shower at work have mentioned that the trick is to shower in the morning before you go, which means your sweat won't smell as bad when you get there. (bacteria makes it smell worse) Then, they bring baby wipes and deodorant to work and clean up in a toilet stall or one-hole bathroom.

Search this forum for 'shower' and I bet you'll hit paydirt. I remember a few such threads just from the last couple weeks.