Yes, yet another thread. Jazz bass. Entwistle Neodymium single coil pickups. CTS 250k pots, Switchcraft Jack Socket, .047uF PolyDrop cap. Very loud and powerful. Also a bit noisy. No grounding issues - touching the string or bridge and dead silence. I let go and glorious 60 cycle hum starts. Shielding can only do so much. Do you guys just live with it?
without any hum cancellation via an opposing coil, it's what single coils do. a gate might help -a little.
Dummy coil! Active or passive bass? My sense is that for active basses, adding a small dummy coil with lots of turns can work well (kills hum, doesn’t change the tone). On a passive bass, such a dummy coil would change the sound. The solution is to wind a large coil (large in diameter) but with fewer turns. It kills hum and minimally changes the sound. Commercially available from Suhr (possibly others), but seems easy to make on your own. The only problem is finding a place for it - it has to be on the same plane (and ideally close to) the pickups. Under the pickguard seems the simplest... Or in a back routed cavity (a large control cavity could work).
Your issue stops when you touch the strings/bridge/metal - your getting RF interference and your bass requires shielding. 60hz (single coil noise) would persist when you touch the strings/bridge. It would only lessen when you balance the pickups.
Putting in a dummy-coil would be a waste of time if touching the strings takes away the noise. It's not just radio-frequency, it's EMI: (Radio-Frequency Interference) RFI vs. EMI (ElectroMagnetic Interference)