I'm not sure of the pickup config for all of the basses, but I think at least one of them has a noise-canceling pickup.
They have all played through the same amp to date, which I suppose could be the problem. It's an old-ish Fender amp with two inputs, a 1 x something speaker (probably 12"), and this fuzzy, cream-colored exterior instead of tolex. The amp output is then taken and put through a DI box and run through the snake and into the mixer. In that way, the amp only serves as a head for the house and a monitor for the bassist. For power, the amp is plugged into a Furman power conditioner that serves all of the PA gear on stage (e.g. digital snake, power amps for monitors, etc.).
I don't know if 1) the buzz stops when they touch the strings or 2) if turning the bass angle changes the buzz (i.e. if it's electrical interference). My instinct is to say that 2 is a no, but I'm unsure of 1. I'll check in future weeks.
In writing this, I'm realizing that I don't have a ton of information, but I guess the first step is knowing what questions to ask and information to collect. Any other info I should gather for troubleshooting purposes?