To me it all falls on what the definition of 'vehicle' is. So I looked it up
online. And this definition seems to fit the best:
4: a means of carrying or transporting something
The bicycle is transporting you. Just as a skateboard, sled, or truck can be a vehicle. So I would say that if pressed, you could be fined and your gun confiscated. But that is just interpretation and opinion.
But it is my feeling that whenever you plan on open carrying, it is also a smart idea to have a LTCF. Because there are instances like these that you may not think about, that a sneaky cop could get you on. And like Frenchy said about someone offering you a ride. Or even if it gets hot, you un-tuck your shirt to wipe off your brow and your shirt tail falls over the gun for a second. Right there you were attempting to conceal the weapon (in a cops eyes). So your best bet would be to CYA and get a LTCF.