If the noise goes away when you touch the strings or bridge, I'm less inclined to think it's a grounding problem. The bass player is supposed to be part of the circuit. When you touch the strings or bridge the current grounds out through your body.
Does this happen everywhere you go with any amp you plug into? I'd take the bass to a local music store, plug into another amp and see if it still does it.
If so, personally, I'd rip the wiring out, sheild all the cavities and wire it back together using a standard wiring diagram
http://www.guitarelectronics.com/cat...ringresources/
Or if you're not partial to the bass, sell it and get a new one.