Edwin was using the abbreviation for a capacitor. I agree it sounds like that, maybe a bad solder joint or component lead, a broken wire or other bad connection.
You said you've sent all of the electronics to Alembic for testing? If there was something wrong on the boards I suspect they would have found the problem.
Has your tech put a scope on the electronics to see if he can chase down the problem? With a scope, no guitar chord and power switch of the jack shorted does the bass still make the popping noise? If it doesn't then I would suspect the jack or its wiring. If it does, have you disconnected the pickups one at a time to see if it is related to one circuit or the other. As I recall they each have their own preamp. How about disconnecting both pickups? The tech should be able to follow the circuit board traces to make a schematic to work from.