You most likely are getting noise from the high voltage inverter used to boost 12 volts to the high voltage necessary to drive the HID. There are a couple likely paths that get this noise into your AM radio: 1) RF radio frequency in the AM band that is being picked up by the antenna as an AM broadcast.
2) power line noise that is being picked up by the I.F. or audio amplifier sections in your radio. That's the most likely source.
Note in the following discussion, I haven't bought my HIDs yet. I am shopping them to use as landing/taxi lights in an experimental airplane but I do have experience in low noise circuit design so here are some things to try...
What to do depends on where the noise is coming from. My first guess would be conducted noise on the power but you can test for RF noise by disconnecting the antenna lead on the radio and turning up the volume. If you still hear the buzz, its coming up the power lines.
In either case, some basic stuff to try is:
Ensure that the ballasts are mounted to metal, with as much electrical contact as possible for good grounding. If you need to, bond the ballast frame to the car using SHORT lengths of wire braid.. not just wire. You can get braided wire at any electronics store or in a pinch, use solder-wick, its made of braided wire. The wider the better here. What you want is to get that noise referenced to the car's ground (a low impedence path back to the battery) and not be radiating around.
Once you have a good power supply ground its time to look at what's doing the radiating into your radio. Where are the ballasts and how far are they from the lights? From ballast to light you have a high frequency transmitter. Those leads should be kept as short as possible.
From the power source to the ballast, the wires are also potential radiators but I would assume there is some filtering at the ballast to prevent noise from being radiated back into the system, cars being so electronic and all but who knows? If the ballasts are noisy, the point at which you pick up power is important. Everything that is connected along that particular power line between the battery and the ballast will 'see' the noise. Obviously, the glove compartment light won't care but the radio might. So, it may be handy to run a separate BIG wire from the fuze block to the HIDs and be sure its not shared by any noise sensitive equipment.
Here's how to look at it.. Your battery is the source of all things. It has a hard connection to ground and provides power along many, many paths. Think of them as loops, with power going out on a wire and coming back through the frame of the car. You can have noisy loops and quiet ones. The trick is to provide noisy loops with thier OWN way back to the battery/ground points. Any device on a noisy loop will share in the noise and AM audio is one of the most sensitive, so make sure you are not sharing there.
To stop the noise at its source, you also might try a power line noise filter like those that Radio Shack sells for car stereos. Its designed to stop noise from getting into radios but will also stop noise from getting OUT of noisy devices like ballasts. If you go this route, mount it as close as possible to the ballasts. Again, big braids to ground.
For the record, on the plane, my HIDs will have their own power and grounds (wires, not the frame) from the battery with thier own fuze. In that way, conducted noise will be confined to very short shared lengths of wire. This conflicts a bit with what I said before i.e. hard grounds to the frame of the car. It DOES mean that the ground currents are shared but it should be OK. The plane will have a lot of very sensitive avionics in it and the effects of noise there are not something I want to consider..
So.. keep the noisy stuff short, run dedicated power lines, install filters close to the ballasts and make sure you have very good grounds.
If you find it IS RF.. interesting.. the FCC would no doubt like to know about THAT. But, you can try shielding the wires that go to the bulbs with copper foil (wrap them and connect to ground with a short braid). But if I got that far.. I think I would send em back and buy something else..
There IS just a small possibility that the actual arc of the lamp is radiating in the AM band..... but wrapping the lamp in foil is probably not an option :) In that unlikely case, I would consider a better AM radio. XM or Sirius.. very nice..
Hope this helps..
RJO