On the older part of our home, we have experienced electricity running through the bath tub fixtures only. (water is provided by a water pump) We have had two electrician look at the problems, they checked everything from the grounds to the neutral(?) Now the ground is hot as well. Help!

Breakers need to be turned off one by one until voltage is gone. This is the culprit.
Could be pump shorted or leaking to ground. If the ground was intact, it should trip breaker.
You may have bad ground and bad pump.

What, if any electrical work was done prior to you noticing that your plumbing outlets are Hot? Do you have to grab both knobs in order for you to get it by the voltage? Do you have a meter that you can test the plumbing knobs with to see if there is actually voltage on the fixture? Have you inspected the cold water bond connection point near your Main Panel to make sure it is still connected.

Sounds to me that someone did some work for you and managed to put power to your cold water pipe.

When you told the electricians, what did they say was the cause?

Have you called the city or county electrical inspectors and ask them to evaluate the failure?

Down here The Electrician is the person that would do what was in first Post. Then it would be further dermined it may be bath circuit wire touching pipe(Rat will expose live conductor, nails and staples can pinch wire to ground. If power goes out to plumbing when light switch is turned off, you know a hot is touching ground between switch and light.
Turn off breakers one by one WILL determine source(circuit) of problem. Inspectors don't do this,
Electricians do. Down Here.
Had one customer getting shocked and it turned out to be a pinched phone wire with the bath tub.