To the OP.
Please, before you spend a nickel on any “solution”...(well, it’s yer money, do with it as you see fit, but...)
There could other issues causing the hum in your bass that isn’t the fault of the bass. Being a bassist and a semi-retired pro audio guy and PA trouble-shooter, I go through this exercise on a regular basis.
Do 2 things....as you are hearing the hum, mute your amp, unplug the instrument cable from your amp and see if the noise is till there. You can unplug your bass, unmute your amp with the bass unplugged and see if the noise stays or disappears, too. If the noise completely disappears, then plug your bass back in, get the hum going again, and re-orient your body and bass in different directions and see if the hum changes louder or softer as you face different directions. If you are getting him, there is an external source causing the hum. RF hash from nearby lighting fixtures, bad lighting dimmers, all can cause problems with noise. As @walterw pointed out, if RF hash is entering the pickups, then a wireless unit won’t prevent the noise. If a wireless unit. DOES solve the problem, then good for you, but there’s still an issue downstream of your bass that needs to be addressed. It’s really helpful to call in an audio technician well-versed in diagnosing (usually 2/3rds of the battle) and solving such issues, but like anything else, that won’t be cheap.
There is a mind-numbing number of churches out there that get great and wonderful modern upgrades, but sometimes, new and existing equipment is used and mixed together that can cause issues, or the installers miss a little details with regard to wiring, implementation of the system, or just plowing through the install with no regard for the instruments being used, particularly single-coiled-equipped guitars and basses. It seriously irritates me when I hear an “audio tech” callously tell a player, “you need humbuckers in that there thing!” Because they are too lazy to check behind their own work. No doubt, humbucking pickups can be a great help with extraneous noise, but I personally haven’t found a Jazz bass humbucking pickup I like. By the same token, it’s our responsibility as the players of single-coil instruments to make sure our instruments are in good condition and well-shielded. And frankly, there are situations without much of a fix, such as a player with, say, a very old, very nice vintage instrument that anyone would be hesitant to tear apart and start taping copper foil all over the place inside. Even though it needs to be considered if the instrument will be used in modern playing environments, I’m not about to diss a player for his reluctance to this. I’m fortunate enough to know how to thoroughly shield a bass, and now I own a very-well-built and shielded bass equipped with single-coil Jazz pups that I very seldom ever have noise issues with.
Most always, a fix can found and compromises made to quieten things down, but it does take some working knowledge of the tech side of things. And not from wildly-varying opinions and suggestions on a public forum (sorry).
Been there, still going there when I can...