It isn't a grounding issue, you have a shielding issue. If you have a grounding issue it would get louder when you touch metal/strings/bridge, a shielding issue goes quiet when touching metal/strings/bridge.
You need to give the bass a proper shielding job, you can use either copper foil tape or conductive paint. I prefer the former because I can source it locally from stained glass supply shops.
You need to line the control cavity, the pickup cavities, and the pickup covers with foil tape. Do the control plate as well if it isn't already conductive. I bring up the foil tape over the cavity edge so you can pierce the foil with the screws. Then you need to connect a ground to your shielding and ground your pickup cover shielding to the control cavity shielding. Don't forget to add a ground wire to the shielding in all cavities, all the shielding must be grounded to work. When doing pickup surrounds I like to bring the copper foil around to the outer edge so I can solder to it more easily.
It is an easy fix but it will take at least an hour your first time. I hope this info helps, I personally hate hum so I do what I can to remove it even from basses I do not own.
Carvin LB76 / Dingwall ABZ ! Support Local !
MarkBass SD 800
Epifani UL2-310 / fEARful 1212/6
! Rocking against all gods !