Floating Ground in Renovated Bathroom
fed from an obsolete GE sub panel with no separate grounding bus. I had new Square D breakers installed in the sub panel.


Am I reading this right that you put Square D breakers in a GE subpanel?  Who did this work?

You can't put random brand X  breaker in brand Y panel.  Yes, I know some will "fit" and feel like they snap in, if you completely ignore what insertion force is normal. But the buses won't match up, and they will arc. 

If you stick with the OEM breakers/panel combo, those are UL listed to work together.  UL will also classify certain specific breakers to work in certain specific other panels: Take the 3/4" wide Square D "QO" panel. Eaton CHQ (not CH) or Siemens QD breakers are UL-classified because they have passed design review and every safety test. 

Are Square D HOM breakers classified for GE panels? No they are not, they are definitely not. I know that because Square D has decried the entire concept of classified breakers, condemns use of ANY other breakers in their panel, and refuses to make classified breakers for anyone else's panel.  

So those breakers definitely do not belong in that panel.  Now if you get us photos of the panel and particularly the labeling, we have experts here who can tell you exactly what breakers are UL listed (or classified) for that panel.

Yeah, yeah, your guy has been doing this for 20 years and never has any callbacks on any of his alien breaker swaps.  That he knows of. 


  the electrician used the existing feed from the GE panel, thus no ground. The light fixtures and outlets all have ground wires connected together but this ground is just floating. When I bring mu induction tester to the vanity fixture it beeps, even if the wall switch is off.


Where is your induction tester getting a ground reference?  can you try it with a solid ground reference taken off a panel cover? Any wire will do to bring ground for testing. Phone line, ethernet, RG58, whatever you can lay your hands on.   


  He installed standard duplex outlet just outside the bathroom connected to this floating ground.
  Apparently enough coupling from ground to neutral exists to allow the ground test neon light to illuminate in a tester so the circuit read good. 


Are you sure? That would be an awful lot of coupling.  I have never seen capacitive coupling deliver enough EMF to move the needle on a mechanical voltmeter, nevermind light a light.  That's why we see it  reported so much of late: modern DVMs are sensitive enough to detect it.  


  A home run to the bathroom would have been easy when the walls were open, other new runs were installed within a few feet. Don’t know how they missed this because I told them at the start that I didn’t want shortcuts and wanted a real ground in the bathroom. 


Are you entirely sure he didn't retrofit ground? That is perfectly proper and legal as of 2014 NEC.  There is no need for the ground wire to travel the same route as the conductors, since ground wires only carry fault currents.  

In fact, a ground retrofit doesn't even need to go back to the panel.  It can reach anywhere that has a ground wire that is thick enough, though it's supposed to be something served out of the same subpanel.  It can also go to any non-flexible metallic conduit, or the grounding electrode system.  (Not water pipes, though). 


  I’ll try to route a ground wire to the new dryer outlet on the other side of the (concrete block) wall.


Maybe that's what they did.  

But do it also, sure.  Worst case you have a redundant parallel ground, and that is allowed because current only travels on grounds during fault conditions. (DON'T use the same logic to parallel anything else).