Info on how you are using the bass is important.
if you are using the pickups unevenly, you're going to get some hum. This is a just the nature of the single coil pups in Js. Blending the neck and bridge equally eliminates this hum (the two pups together act as a humbucker)
If you're getting noise when the pups are equal, try moving the bass around: rotating it in all three dimensions. If the hum changes as you rotate it (gets softer when you turn it this way, louder when that way) then you bass is picking up background electrical fields. You can reduce this by turning off extra electrical devices, lights and monitors for example. If you have lights on a dimmer, those are big culprits. If you're standing too close to your amp or to a power outlet, that can add some hum also, again from background electricity. If you're willing to modify your bass, check out the discussion on shielding that Atoz linked to above. Shielding your bass is a more permanent way to get rid of background hums. This is especially useful if you gig places where you pick up a lot of background hum.
If the bass hums when you're not touching it, but gets quiet when you touch the strings, or a metal part, it needs to be grounded. The bridge is usually grounded in J basses, if I remember correctly, but who knows.
Finally, if you pick up hum from turning up your tone, and/or both pups, and it's not background electricity, you may look into replacing your electronics, as cheap or faulty electronics can add a hum to the sound, and this will be magnified as you turn up our highs.
EDIT: I forgot, you're using it with GarageBand. You may also be getting a hum from the wires or computer electronics, especially if you are using a computer with a built-in sound card and you are just running into the mic in. If you're using a cheap cable going to the computer, it might not be shielded, and can pick up background hum, just like your bass. Shielded audio cable (1/8", 1/4", whatever you're using) is readily available at Guitar Center, or any electronics store. If you're using a built-in sound card, remember that is is sitting in the computer, right next to all of the other electronics, it may be picking up a lot of hum, especially since built-in cards are made more for recording from a computer mic, not a line in or high quality mic.