My normal way of learning a song is to work out the overall structure first - I listen to the song without an instrument in my hand and right down the chord structure (eg I / / / | IV / / / | V / / / | II / Iv / | etc). At this stage I don't even know what key it's in (which I find useful as the bandleader may decide to do it in a different key anyway). Having done that I'll listen to the bass part - here it's useful, as everyone else has said, to understand intervals and major and minor scales (for the music I play I don't need or want to know about modes). Singing along is good too at this stage. I might write stuff down at this stage in notation (I'll have ascertained the key at that stage, either by playing along or looking it up) - but only if it's particularly complicated. And finally I'll play along - usually I'm not a million miles away. I have been know to learn a song and turn up to practice and actually play it for the first time at rehearsal - usually with a reasonably close result.
Of course it all depends on the type and complexity of the music. One advantage of my method is that if the bandleader changes key, or changes the song structure, its easy for me to adapt.