Gidday there Paul,
Long time no see!. [Linked Image]
Well here's one for the books, I can't say I've heard of anything like this before.
Only advice I can offer however, is, it may pay to check the Neutral connections at the Main switchboard, as I have a feeling one of them may be loose.
Just a wild guess.
Only other thing I would suspect, which is even more remote, would be RF currents getting into the pipe-work.
BTW, is the bath body bonded to the drain?.
I'd get a voltmeter and test to a known Earth point, something sounds a bit wierd here. [Linked Image]