I might know a thing or two about this. Don't be so sure it's the amp.
A little bit of structured troubleshooting will help determine where the problem may be located and just as importantly, where it is not. The fact that the noise goes away when you touch the strings or bridge (which are electrically connected) is a clue by itself, which suggests that the problem is external to the amp.
1. With nothing plugged into the amp (no bass OR cable), is the noise present or not?
2. When the noise is present, does it increase and decrease with the amp's input gain/volume control? If it does change with the amp's volume control, now do the same with the volume control on the bass. What are the results?
3. Does the noise change when you touch the metal shell of the 1/4" plug on the bass end of the cable? How about on the amp end of the cable?
4. Is the bass you are using active or passive? Are the pickups humbuckers or not?
5. Is the amp connected to a properly grounded AC power source? Is the power cable undamaged? If you are using a power "conditioner", remove that and try again.