What you have is pretty common. It's caused by your body not being grounded. The human body is a good antenna for radio frequencies or electrostatic interference and your proximity to the pickups will inject the interference into them or the other signal paths in the guitar. When you touch a grounded part of the guitar you're grounded through the cable, amp and wall socket and the noise you pick up is shunted to ground.
Common items that generate this type of noise are fluorescent lights, anything with a microprocessor, light dimmers, some amplifiers or effects, etc.
Fully shielding the electronics in the bass will probably help, if they aren't already. I'm not saying that you may not have a bad ground but that normally causes hummmm rather than buzzzz. Try a different cable too. Ya never know, it may be providing a less than good ground from the amp.
mech