Do you want the bicycles to stand up or are they to be flat against the sides or top of the cake?
If they will sit flat on the cake, one way to make them is to use a chocolate transfer - Liv and Kaye Hansen go over this method in excellent detail their book Whimsical Bakehouse. She’s amazingly talented with chocolate transfers, and it would be easy to do once you found a graphic or photo or clip art of the kind of bicycle you want to do. If you go this way, it will help if you coat the entire back with white chocolate for strength and support. Make more than one; in fact do three.
If you are doing it so it stands up, you need some support. One way is to make a bicycle cookie, and decorate it on both sides.
If you want to model it from gum paste, I would form the bicycle body and handle bars from wire, and cover it (you can find wrapped wire at the craft store. I’ve seen it in green and brown. If you want the bike to be a different color, you could cover it with fondant once you shape it and then paint it. But that won’t look very sleek.). You can form the wheels from black fondant mixed with some gum trag so it dries faster. you’d cut the circle, then use small rectangular cutters (sold from Squires Kitchen in the UK) or an exacto knife to cut the centers to make the spokes. The bike body would probably need to rest on the tires. I guess that would depend on what kind of bike it is.
I would probably not try to push my luck that it won’t break by planning it so it leans against something. Sounds like fun!