I always approach my part in the arrangement as its own part. I was trained in classical piano originally, and in the that music, the left hand was its' own part, not just a collection of roots and pedal points. The same as orchestral music, or string quartets, or 4-part vocal music.
My favorite players, from Carol Kaye and McCartney, on to Anthony Jackson and Jimmy Johnson, always played parts that could almost stand alone. They grooved, were the foundation of the song, locked with the drummer, and had these little figures that echoed some other part in the juiciest spots.
This was my inspiration and target for my own development. I always felt bass was an 'ensemble' instrument: It was the mesh of the whole band that was the rush. As much as I admire Jaco or Stanley, it was utterly out of sync with where I saw myself. My goal was when you came to see a band I was in, you might not even see me, but you couldn't sit still in the face of that much groove. I still keep shooting for that.