Hey Andy, that is a weird one. Can you isolate it to one pickup or the other? Assuming your bass has Signature electronics, hard pan to one or the other and see if it makes any difference.
*Kind of a long-shot; but pop the backplate off and see if any of the pots or switches have worked loose, and may be making poor contact with the shielding. I've never heard quite the sounds you have, but I have heard some funky noise from this.