You have a grounding issue. Here's how to tell: If your bass hums once you touch the strings (but is otherwise quiet), you have a grounding issue. If your instrument hums but becomes quiet once you touch the strings, you have a shielding issue.
Why does my bass make a buzzing noise?
The neck of your guitar or bass should have some 'bow' in it. In other words it really shouldn't be perfectly straight. Fret buzz is generally caused by some combination of not enough bow in the neck, the bridge string height being set too low, and possibly a warped or irregular neck.
Why is my bass amp humming?
A healthy amp is likely to make some sort of noise when idle. ... Poor quality pedal boards, FX units or even guitars will feed noise into the amp that will be exponentially amplified. If the AC supply is poor or your outlet is not earthed well enough then it can create a humming or buzzing sound.