I used to have a '51 RI. Great bass!
I put a Seymour Duncan SCPB-1 into it and shielded it with the copper tape. As well as taping the cavities, tape the underneath of the scratchplate (making sure it touches the tape on the cavities) and the run of cable which goes from the pickup to the controls.
Might be little OTT, but I never had a buzzing problem after that.