True bypass+power supply=noise?

[Ed G.]

I was having some noise issues in my house, and trying to isolate the cause, I went to my pedalboard. It's powered by the Visual Sound onespot adapter. I noticed a lot of the noise went away when I unplugged the adapter (and all of the pedals are true bypass, in bypass mode)
I think that even though the pedals are bypassed, they still share a ground with the circuits in the pedals, and that's part of the noise problem.
I know part of my problem is the power in my house. It's an old house, has two-conductor wiring, so it's not truly grounded. But still, what can be done to minimize this noise? I notice the noise goes away for the most part also when I turn the guitar volume all the way down.