The ground lift switch on a DI would only help if you have hum when the bass is on standby. That relates to a voltage potential or "ground loop" caused by your power supply, your amp, and the mixing board on the other end of the mic cable being connected to different power sources. Sometimes that will make your amp hum, or make the input to the mixing console hum - and lifting the DI ground can sometimes resolve it.
What I believe we're talking about here is also not an issue that involves DC leakage onto the audio line. (DC by nature is not hum but causes other odd issues).
If your bass is dead quiet in standby but hums when you turn on the pickups, and varies as you move left and right, then it is simply your large single coil pickups "hearing" and amplifying ElectroMagnetic Interference which is generated by poorly shielded electronics or AC sources.
Get your output levels set to an agreeable volume, go through the hum balance procedure, find the quietest direction to point the headstock, and THEN decide if your noise floor issue needs further attention or if it's something you can live with.
We all hope you will spend as much time as possible playing and enjoying that bass. Try not to get caught up obsessing about details. Make music!!
Jimmy J