If the hum goes away when you touch the tuners, strings or bridge, it sounds like a grounding issue to me.
I'm certainly no expert, but I just wen through this.
Before you start tearing anything apart, try a different instrument cable first and go straight to your amp - I'm assuming that this hum only occurs with the bass.
If you have a Volt/Ohm meter, you can do a couple of quick continuity tests to see if maybe a solder joint for one of the ground wires may have broken off. Set the meter to read Ohms and take the control plate off the back of the bass. Place one lead of the meter on the bridge and then check all the ground (usually black wires) solder points on the back of the pots as well as the ground lug on the output jack.
If the meter doesn't read "zero" (0.0) or shows "Open", then you can start isolating backwards in smaller segments.
If you isolate just the bridge ground wire and get a bad reading, take the bridge off and check that the wire is still in place where it makes good contact with the bottom side of the bridge. A tip that I got here on TB was to put a piece of shielding tape on the bass body under the exposed bridge ground wire and also put another piece of shielding tape on the bottom side of the bridge - essentially making a shielding tape sandwich - where the bridge ground wire sits.
Best of luck.
The root of the problem has been isolated....
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