"I dunno...
Ripper said:
I seen this used before too for similar circustances with amplified acoustic guitars. Take your cable that goes from the Bodhran to the amp. Pick one end and make sure you mark it somehow. This is the end that goes to your Bodhran. Cut the ground wire connection at this end. The ground wire on the amp cable then becomes ground-relative to the amp. I'll bet it's the battery pack that is causing the issue. Doesn't take long to try it and you can always put it back to normal quickly. It may not work, but it might just be the ticket too.
If you do this, where is the signal return path for the pickup? It sounds to me like you're describing having only one wire as a connection to the pickup, unless I misunderstood. You can do this with shielded wires inside an amp or with connections to a reverb tank but that's because the ground signal return is through the power supply. With the Bodhran it sounds like hanging a light bulb up by only one wire and trying to light it is the equivalent of your model. Then again, I just got up and my brain may be too fuzzy to understand what you said.
The previous post asked "So is the mic acting like a single coil pickup, i.e when you grab the strings the hum is reduced, but when you let go the hum comes back?"
The short answer is YES! Of course, there's an extra kicker. Any metal surface like a chassis, the shield on the outside of a connecting cable or the strings on a guitar (which are normally grounded through the output jack and cable back to the amp) acts like an antenna to pick up the AC hum in the air which comes from all the AC wiring in our world.
Making sure the unit has a good low-impedance ("resistance") path to ground through the power cord and house wiring dramatically reduces the hum. If the home wiring has a ground problem then the induced hum currents are not drained on the outside by an easy path and instead find other paths more to their liking, like through a gain stage inside the amp!
http://www.guitarnuts.com has some good FAQs about this. Think of the bodhran as like a guitar and the info applies in the same fashion.
http://www.aikenamps.com has some great FAQs to do with grounding methods inside amplifiers, if you want to dig a little deeper. More than you need for this problem but invaluable if you sniff the solder inside amps.