Better tone with you hands?

Practice to use a lighter touch and to opti-/minimize your finger movements.
Let the amp do the volume work.

Try to pluck the string so that the string vibration is mostly parallel to the body.

A little finger vibrato can add to the sound. Classical vibrato, not blues (bending) vibrato.

 

One technique concerns humbucking pickups. Each coil picks up the string frequencies at two different points.

If your technique is such that the string vibrates up and down above both pickups, the fundamental and lower frequencies are doubled and gives you a more round, mellow, sound.

If your technique is such that the string moves down on one coil while it is moving up on the other, certain harmonics are cancelled.

I don't really know how controlling the patterns strings move in is accomplished. It just came to me after years of varying my techniques in search of fine tone.

 

this does come with experience, it's 90% technique and 8% knowing what the specific bass your playing is going to sound like when you apply said technique, and 2% magic, superstition and random quirks of the universe.