Buzz vs hum can be two different things. Many people confuse the two.
Buzz tends to be more harsh and raspy, whereas hum seems smoother.
That being said the perception of one vs the other can be subjective, so its more like a continuum rather than being polar opposites.
Given that, would you say it's more buzz or more hum?
Does the buzz/hum come through the amp. (Sounds like a dumb question but I have my reasons.)
Does the buzz/hum go away when you touch your strings?
Do you have single coil pickups? One or two?
Maybe tell us what bass you have and is it stock or been modified (to the best of your knowledge).
Do you know if the the bass has any shielding in the control cavities? Sometimes it's hard to tell as a stock bass may have shielding paint that's not easily recognizable. Add on shielding will be copper or aluminum and usually pretty easy to spot once the pick guard or cover plate is removed.
Is the buzz/hum present (or does it change) when the instrument cable is disconnected from the amp?
Does the buzz/hum change when you face a different direction?
Have you tried a different instrument cable?
Do you know someone with a bass or guitar to try in place of your's?
Are you absolutely certain that there is a good ground at the outlet where you plug in the amp.
(This would require a tester.)
Have you powered down (unplugged from the wall not just shut off) all other electronics in the room other than the amp?
Do you have light dimmers, does the dimming level affect the buzz/hum?
Take the amp to a different part of house, or wherever you are, or take it to and entirely different location.
Does the buzz/hum change?
A lot to work through but it can be very helpful to those of us on TB who might pitch in and offer suggestions?
Thanks.