Ben,
At the moment, I've got a smilar problem with my 75 P bass
Just this morning, I touched the top of the jack that plugs into the bass,.and there was the buzz again!......it happens if I don't touch the strings, or touch the pole pieces of the pup.
I posted this ages ago, and got the response ie..the grounding problem!!
So.to continue..I knew it was just a grounding problem, but at the moment, I'm unemployed, so can't put the bass in to Jimmy Moon in Glasgow (the only guy I'd trust in Scotland).
SO........when I touched the jack....(meant to be insulated in rubber and all that!)........there was the buzz again.....just like with the pole pieces!
So......by chance........I touched the bridge at the same time. Result.......One Quiet and great sounding P bass
Would appear to me (as Adriaan and others pointed out) that the problem most probably arises from the ground under the bridge, or the connections to the jack!
Hope this helps.
BTW....I still use the P bass for most live gigs at the moment..............just keep a hold of the strings when not playing!
Funny though.........last week , I never heard a buzz from her.....strings held or not...but at home, you can hear what needs to be done.
George