Somehow, I can't get past the thought of electrocution.

I don't see any difference to your fridge or whatever other metal cased appliance that is Earthed, and the power supply is effectively an isolation transformer unless the primary somehow open in spectacular fashion.

On the other hand, I've been shocked before, and it was scary.


Is this a suitable frequency counter to connect to it?
http://www.jaycar.com.au/productView.asp?ID=QT2202
I'm on a bit of a budget.
Some frequency counters are actually called "RF Frequency Counters"
Is there any difference in their interface?
When I connected my scope to my radio, I could see stuff,
but the radio made noise the whole time it was connected to any part of it.

 

I don't have my fridge sitting on the foot of my bath tub.

 

I don't have my fridge sitting on the foot of my bath tub.

There are other possible reasons for that.
Power transformer going up in smoke for example
No real reason to have it in the bathroom for fear of electrocution,
geo-location makes no difference, the exhaust fan in the bathroom does.

People have taken it to much further unnecessary extremes:
https://www.youtube.com/watch?v=C_6bh90_c6w

 

Need to do the Huff Puff technique to stabilise the oscillator:
http://www.youtube.com/watch?v=Y1pfd1I9veU