Not all antennas require a ground plane. A basic antenna like a dipole is self-contained and requires no ground plane. The concept of a ground plane is roughly to build a antenna half as long as a normal self-contained one, then add a mirror so that it looks like a complete antenna from the antenna side of the mirror. We call this mirror a ground plane. such antennas are more compact, but don't work right without the ground plane (mirror to make it look like a real full size antenna).
So your first order of business is to find out what kind of antenna you have. If it was meant to be mounted on the top of a metal car, then it very likely requires a ground plane. A good ground plane extends about a wavelength underneath the antenna, although less can be used as long as this is taken into account when the antenna is designed, else the impedance won't be as expected. CB frequencies are in the 27 MHz range, which means the wavelength is 11 meters. No car has a roof 22 meters accross, so a car top antenna will have been designed with a small ground plane in mind. A metal sheet about the size of a car roof, or a bit bigger if you can manage it, should do fine.
If you have or end up getting a self contained antenna, then it is best to keep it away from anything conductive. It is meant to work on its own, so conductors in the near field will mess up its resonance and change its impedance. Again a whole wavelength clearance would be great, but in reality you can live with less.
If you really want to get into this, get a SWR (standing wave ratio) meter and experiment. Some transmitters may have SWR meters built in already. If you want to get into this some more, you can measure what the antenna impedance is, know what load the transmitter wants to see, and put matching components in between so each side sees a nicely matched load. There is something called a "Smith chart" that helps with all this, but that's serious decent into the black magic of RF.