Is the hum louder or quieter if you touch the pole pieces with your tongue?
If you do the above in the basement with bare feet, does it:
1) Hurt
2) knock you on your ass
3) kill you
If we don't hear back, I'll assume number 3 and you're problem is essentially solved, though not in the way you preferred.
Grounding. Ground wire from pickups and in some basses the bridge, should be connected to case of pots (not to mention one of the pins), as well as the sleeve of the 1/4" jack.
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Dan Duran
That 80's BandAlesis Fusion 6HD, Korg Triton, Roland JP6, XP-50 & SC55, Moog Opus 3, '85 Steinberger XL-2, Michael Kelly Bass, Epi Explorer