Experiment with your own suit, but a decent wool suit should come out wrinkle-free. Just roll it up carefully. The hard part will be getting the shirt there without wrinkles. Either pack a brand new shirt (still in the pins and packaging) or buy a shirt after you get there.

But rather than taking the bike to the wedding, could you just get a ride from the bus depot? At most weddings, they expect to have to pick up people coming from out of town.