I can tell you what NOT to do.
I would NOT advise that you, if you are traveling between say, school and home, carry your suit in your left hand, with your right hand on the pedals. It turns out if you need to brake suddenly (because, for example, your suit bag got caught in the spokes) and brake with your right hand only, it stops the front wheels, sending you over the handlebar. You might then need to go visit your friends in med school for a consult.
On the other hand, may I say that those plastic suit bags Brooks Brothers send you home from their store with - quite sturdy! Impressive. Bag slightly ripped, suit fine.