I don't have the Bose system (thankfully, as I'm not a big Bose fan), but here are a couple of suggestions...
Try *loosely* covering the port on the front of the box to dampen the harmonics from the air being pushed around..see if that makes any difference. Also, the enclosure uses down firing speakers...try raising the height of the enclosure by placing some spacers to lift the box slightly above the shelf. Finally, it could be just the enclosure itself resonating, if that's the case, not a simple fix (requires some re-engineering and changing the speakers).
You mentioned vibration...it could be that the box is just not firmly attached to the shelf...but I was reading between the lines and assumed you meant harmonic vibration.
All told, the simplest solution is just to unplug the sub.
. FWIW, I am perfectly happy with just the doors providing bass, but then again, I upgraded the door speakers and am using passive crossovers...which I suppose would be another suggestion: you could add a crossover to the line and dial up the Hz until the drone disappears.
I guess my brain is not processing as logically as it usually does...I suppose the first thing I should have asked is if this a "new" issue or if it's just always been that way. Duh.