Good question.
I want to achieve two things with my bass playing.
1) I want to be able to lock in with any drummer at a jam or proto band, and form a competent enough pocket that it feels like a 'band' rather than two instruments.
2) I want to be able to write basslines that are interesting, that would be a bit different to what another bass player would have written. That is to say, my presence in the band is positive not only because I hold it together and make it sound nice and band-y (as most good bassists could) but also that I bring enough of my own personality to it that I feel like I'm putting a stamp on the music.
I don't really have the same heroes as most people on this board - I'd be Peter Hook or Kim Deal over Jaco or Wooten. I most admire the kind of bassists who write recogisable lines, but people who don't even know what a bass is still dance to their music.
As I get better, I become more aware of my flaws. When I started out I had no awareness of just how out-of-time I was playing. As I play better and better in time, the slivers where I am out of time seem bigger and bigger. Does that make sense? So the better I get, the larger the mistakes I make seem, relative to the objective errors.