Since all the basses do that, it's time to look elsewhere. What amps are used? Are the guitars amped but the bass DI? Did you try a different cable? Also, P-bass pickups will cancel their own hum, but J-bass pickups won't unless you use both Js together. This is assuming that they are not noise-canceling pickups.

We have a problem with a ground loop in my church too. We've got a keyboard in the basement that is wired to the organ. Theoretically, the organist should be able to use the keyboard for piano/harpsichord sounds. Problem is, we get a nasty hum through the speakers for the organ if we do. The people who installed it years ago "solved" it by defeating the ground on the keyboard altogether which is not particularly smart. I also got one when we got an original PS3. It had a three-prong plug. We'd get hum through the T.V. Turned out that the cable line was not properly grounded.

Ground loops happen when electronics have more than one route to the ground. See Wikipedia for more details, the source of all things truthy.