Which exact Sansamp model is it? Google brings up several possibilities, but not one that is definitively the model you describe.

What's the make and model of the amplifier?

Do you get the hum only when an instrument is plugged in?

Do both the RBI and the amp have ground connections via their respective mains cables to the same mains outlet?

Ah, my bad.

It is the RPM bass pre (not RBI), and it's going into an Ampeg BA112.
I'll check the plugged in question later.
No, they are not on the same outlet.

OK, I found that one, although I wasn't sure whether there were major differences between the standard and the bass models. Either way, both the BA112 and the RPM take an IEC mains plug, so I assume that the chasses on both the them is mains earth.

With this type of dual-earthed arrangement, it becomes more important to power both units from the same mains outlet, usually by having a small mains socket board or (better) a Y-shaped dual mains lead. This ensures adequate earth bonding, assuming your wall outlets are well earthed.

The final link is the bass guitar itself. It would be useful to know whether you get the hum (a) with no guitar plugged in, (b) with the guitar plugged in but placed in a stand, or (c) only when playing it with fingers touching the strings. If it's (a), then does the volume control on the RPM or the BA112 make any difference to the audible hum level?

thanks dude. can you elaborate on this a bit more?

"small mains socket board or (better) a Y-shaped dual mains lead."

Here are examples from the Amazon (US) site:

This is the mains Y-cable.

This is the socket board.

It took me a while to translate UK "socket board" into US "power strip".

That certainly clears things up! Would running an extension power cable to make sure they are plugged into the same power strip (socket board) work? They are in different areas of the room.

I still have to check out what happens when things are plugged in.

Yes, the idea was to test whether you still got the problem when both units were fed from the same wall outlet.