Freakygreek - Tvad's suggestion is a good one, assuming the "buzz" you are hearing is ground hum. What often happens is that the ground potential between two components is different, causing a ground loop.
What you are trying to do by connecting a wire between the two chassis' is equalize the potential, thus minimizing the loop. You will need to make sure that you are connecting the wire to a grounded point on the chassis of each component. Chassis screws are usually good for this, and there's an easy way to make sure the screw is grounded if you have a meter.
If you have access to an ohmmeter or multimeter, disconnect the component from power and the rest of your gear. Set the meter to read in ohms, then touch one lead to the screw you want to use as a connection point for the wire, and touch the other lead to the outer sleeve of an RCA jack on the back of the component. If the meter zeros out, the screw is grounded. If it doesn't, look for another screw until you've found one that does. The screw is grounded to the chassis, and you can use it to attach the wire.
Your wire should be long enough to connect the grounded points on the two chassis' of course. Since you are trying to equalize ground by giving it a better path, you want the wire to be at least the same gauge as the ground wire in the thickest power cord you are using. So, if your Bryston amp's power cord is 14ga, you want the wire to be at least 14ga. 12ga would be better, but no need to get ridiculously large. Make sure it's insulated wire - bare wire could touch something else and create a bad ground.
Connect the wires as Tvad suggests, and see if the buzz goes away. If it does, you can make it fancy by getting some lugs so that you can more easily connect the components with the ground wire.
If it doesn't go away, and you don't have any other components connected, your buzz is probably not from a ground loop. It's probably from something like flourescent lights or an electric motor on the same electrical circuit. If that's the case, you will have no choice but to move the audio gear onto another circuit if you want to get rid of the noise.
