Bass Guitar (PJ Pickup) NOISE while recording!

There's so many variables it's difficult to give a definitive answer. Single coil pickups are famous for creating hum and picking up line interference. One of the things I keep handy is an old brass belt buckle with a four foot wire soldered to it and an alligator clip attached to the other end. I used to carry this with me to sessions, if my Strat was picking of noise I'd slip the belt buckle in my sock and attach alligator clip to a grounded part of the instrument, that will take care of some of the hum and a lot of the high frequency interference.

Cheaper instruments use inferior wiring & poor shielding.

Light dimmers and some appliances (refrigerators) can cause line noise.

Having the instrument close to computing equipment.

Depending on what you have for a computer monitor can cause noise. If your monitor is separate from the computer turn it off. Yes flat screens can do this, I'm not talking about old CRT monitors, flat screens can cause internal interference.

To minimize low frequency hum the performer can turn in different directions to cancel most of the hum.

Make sure all computing equipment and/or gear attached to the computer uses the same wall power outlet.