Here is my 2 cents. To the op. What kind of noise are you getting? Bass guitars have really low signal. They s/n ratio is pretty bad. The noise you may be hearing might just be coming from the bass itself. Everyone is focusing on what is going on after the bass signal. Odds are it's coming right from the source. His amp is not duplicating it because most bass amps were designed to filter out a lot of noise. But listen closely, part of it is probably there. When you are recording it you have a louder mix in the recording than live. This is why you can actually hear the problem.
If it's a
really old bass or faulty, it might have a poor signal, otherwise I beg to differ:
If the bass is active it will in fact have a very strong signal. Properly working passive basses should have strong signals too, due to bigger strings and pickups.
Most modern bass amps hide nothing as bass playing into the higher ranges has been explored. Older amps to a lesser extent maybe, but you should still hear a faulty signal at the amp if there is one.
In my experience I've encountered way more noisy guitars than basses. Maybe it's guys using older guitars with classic amps, that's just my experience.
If it's a faulty bass, there's a good chance you should hear it at the amp before it hits the desk.
It might be the amp, the amp's DI output or the connecting cable. If you have "ground lift" on the DI it might be worth trying it to see if it helps the noise in your recording.
Solo the bass channel and have a good listen with the bass guitar volume up, but the guy not playing just to see what's coming through.
JL is right about using the MF recording feature though, it's not great at all.