It would really depend on how well you want it to work. Ideally, you want the antenna mounted in the center of your ground plane. Since I doubt you want your antenna in the center, as it would be awful close to any mounted bicycle, you are likely thinking of mounting it off to one side. That will work if, as LtDoc said, you have a good metal to metal contact. Truth is, most of the racks I've seen are either painted or powered coated, and rely on clamping to hold the parts together. This won't make for an ideal ground plane, but it's better than none. Just do the best you can and you'll have to live with it. Likely it will work just fine.
Ideally, you'd bond all the metal parts together, including the car, but that's going to take a lot of work.
Other option would be a 1/2 wave antenna, but that will likely be hard to come by for CB. You used to be able to find them for boats, but if you could find one, it probably wouldn't be an attractive option.
It would certainly be a fun project to play around with.