We'd normally recommend using two different power supplies, but I see how that would be complicated in this case. Could you try plugging the minirig's USB cable into the BeagleBone's USB port? That may improve things a bit.
Another alternative to experiment with is to power the minirig from P9.01 (GND) and P9.07 (GND). Only try this at very low volume and when the minirig's battery is fully charged, because the current available through P9.07 is limited to less than 500mA. If this gets rid of the hum, the proper way of doing this would be:
- power Bela from the barrel jack
- power the minirig from P9.01(GND) and P9.05 (5V)
when powered from barrel jack, P9.05 will have much higher current capability (it is effectively connected in parallel with the barrel jack input )