Don,
Thanks for the replies.
Before I did the bonding, there were three grounded metal systems at the house and none of them bonded.
The panel was grounded with one ground rod just under the panel.
The well water pipes ran above and were connected to the earth via the well, which is about 10 feet from the panel.
The drain water pipes are in dry sand until they leave the house, about 25-30 feet from the panel. From there they run away from the house, but toward the pole the transformer is on.
The transformer is on a pole with a ground rod, about 30 feet from the end of the sewer pipe.
So, over a distance of less than 100 feet in very wet (home is on a lake) soil, in nearly a straight line, we had:
Tranny electrode, sewer pipe, well, panel electrode. The only metal connection was from panel electrode to tranny electrode. The other systems were only electrically connected because they were in wet soil.
The connection to earth for the well and sewer systems were 20 feet or so apart, in line with the panel and tranny electrodes, but there exists only a few inches of difference between faucet and drain.
Several years ago, after I did the bonding, a storm came through and ripped out the neutral. The drop was replaced along with some other lines going to the house. So if the original problem was a bad neutral, there is a relatively new one there now.
I never saw, nor heard any complaints that would lead me to think there was a bad neutral, but there may have been. A small one may not have been noticed anywhere besides the shower.