Hello
1. You could do a little experiment - take a good size sheet of tinfoil - cover entire back of your bass with it - maybe even wrap it around sides - make sure it is connected to ground. If this makes the difference you are wishing for, then we know it works and can start figuring how to get that foil inside.
2. If the guitar cable is long, there might sometimes be difference, if instead of regular cord ( hot + shield ) you use a cable that is made of high quality microphone cable.
Connection in guitar end mono plug
- red to tip
- black to ground
- shield OFF - make sure it is isolated
Connection in amp end mono plug
- red to tip
- black to ground
- shield to ground
The idea is, that signal does not travel in the shield, that picks up noise
Guitar pickups among phono pickups are symmetrical by construction. Both are relatively high impedance + low voltage devices. I can not imagine why these were not wired balanced ( hot + cold + shield ) to amp .
Now this gives me an idea of how to make the bass quieter ( the first cup of coffee in this morning starts to wake me up . . .)
3. If the pickup / -s of your bass have signal wires PLUS separated ground wire - then you could use stereo output jack. Wire the output from pots to tip and ring. Wire the pickup shield, pot shields + bridge to ground. The pots likely have the shields connected to ground end of pot - so that must be separated.
Now if we use this with regular cable, everything is electrically as before.
But if you use a cable with mono plug in amp end wired
- red to tip
- black to ground
- shield to ground
And STEREO plug in guitar end wired
- red to tip
- black to ring
- shield to ground
This isolates signal path totally from ground, that is now connected to your strings, pu-covers and pot covers. They get together at amp input.
This modification is low budget - one stereo jack plus one cable - and some tinkering. And if it does not bring the results that were expected, there is no need to reverse it, since it will work with regular guitar cord.
And while we are at it - the quality of cable - with balanced line level low impedance pro equipment the shield is not that critical. But as the signal levels go down and impedances go up and signal goes unbalanced, the importance of proper shield becomes more obvious. Some guitar cords use a shield, that is like a net - wires crossing each other - leaving 80% of the area empty. The best cables have two layers of tight copper shield wrapped in opposite directions - some have even a thin plastic layer in between to keep those two from rubbing each other.
Example of low q cable
https://www.thomann.de/fi/the_sssnake_ik22.htm
Example of good cable
https://www.thomann.de/fi/sommer_cable_galileo_238_plussw.htm
Before whining how expensive the good cable will be - we must think, that the guitar/bass + amp surely deserve something of equal level.
And good cable deserves good connectors - I use Neutrik
By now I had second cup of coffee - fried egg and delicious sandwiches - sun is shining - temp is about 22C/72F - perhaps time for
https://www.youtube.com/watch?v=D9mSPFw7BXo