Hi iBrecht
What Kevin has said may well be a solution to your buzzing sound problem however it could also be what you originally considered it to be relating to your bluetooth module. If the sound stops when you turn off the bluetooth module then that kind of gives a hint as towards just what may be causing the problem. The fact that the sound also becomes more audible when you touch the outer metallic casing of your mac mini could point entirely in the direction of interference with the signal emitted from your integrated bluetooth, plus you must consider that you only started hearing this sound after you had the bluetooth / airport module fitted!
Moving back towards what Kevin is getting at with the ground loop problem. Are you using headphones or are you connected to an amplifier and then to speakers? If you are using headphones, then try moving anything metallic such as amplifiers, routers, external hard disk drives or anything that is close to or maybe even touching your mac mini which will prevent signal interference. If you are using an audio out to your amplifier, via the headphone jack, then you may be lucky enough to find a small earth contact on the back of your amplifier which you simply need to connect a wire from to a raw metal surface, preferably a pipe or a nail in your wall etc, not the amp or your computer.
If neither of these concepts resolve the issue, then simply get in touch with the Apple store that added your new bluetooth / wireless module and see what they have to say about the situation.
Hope this helps
-Pos