All the above advice is encouraged to be followed: I have been carrying a neatly folded shirt, tie and suit jacket in a bag on a carrier on my bike. So long as the ride is not terribly long, they shouldn't wrinkle. A quick visit into the washroom where you can wash your face before changing out of your riding shirt and back into office clothes should work. My commute is only 20 minutes, so it works for me. Just in case, I always keep extra shirts and ties in the overhead storage over my desk.