There are two general electric bass setup approaches. One is very low action which requires softer string plucking and that results in less sustain. The other is higher action which allows for harder plucks and more sustain.
That's not the whole truth. There is also a third option. Low-middle action and heavy plucking. The buzz as a part of the sound. Not unusual.
"I let the amp do the work not the string." A strange statement. That's not possible.