It can indeed be soldered to ground, on the back of the pot. That's where the 'shield' wire goes anyway. The brass plate under Fender pickups from the factory, is not a shield at all. It is only a grounding plate. To be a true r.f. shield, it would have to completely encapsulate the pickups. Humbuckers with the metal covers, on a typical Gibson guitar exemplify this.
P-basses are quiet, because the pickup is humbucking, as it is wired in series like a Gibson humbucker. Solder the black wire to any common ground, and the white to the correct end leg of the volume pot, and it will work fine. Plenty of wiring diagrams are easy to find online.