+1 Bingo. When I read the question, the instant answer in my head was "feeling" - though I wasn't sure how to explain what I meant. Nice to see that the first response was just that. There is something transcendent about a good bass line. It is the soul of the song.
Structure. You gotta be able to listen to the bassline and tell that there's a progression going on in the song. It should flow too, from one tonal centre to the next. Which is why roots are sometimes all you need.
When you can pay attention to it with ease, but it doesn't distract from anything else going on in an ensemble.
When it makes people who know zip about music want to move, wther that is dancing, banging their heads, sc**wing, etc.
And everyone was being so hideously esoteric about it... C'mon guys, this is music, you know, notes on paper. No feeling here folks, just good old structure just taking the piss...
You must have synesthesia. Or some good psychedelics. I've always wondered how someone "feels" a sound. Just kidding, but surely you can explain what you mean by feeling a bassline? I can feel the music while playing, but when trying to write a bassline, I never think "okay I'm going to feel this one out." A good bassline has to fit the song. It has to support the music, not be boring, and at the same time not take away from or distract people too much from the other instruments (if the others are playing the melody). This all depends on the song, though.