I think interval training is helpful. I've done some of it.
Mambo is right. This is what I've been told. When you learn songs, try to analyze them in these terms. Then when you see those patterns again, they're just those old patterns again. Having the discipline to do this all the time is another thing.
What also helps is your scales and chords. Learning how all the different chord tones (the third, the fifth) sound against the root is key. They help you realize what, harmonically, is a non-distracting bassline. As your sense to distinguish between the chord tones grows finer, you will have more definite understanding of what you hear and of what you play.
I would say that, for most of us, having a great ear is a symptom of having a bunch of other stuff together.
I am only at the point where it is starting to come together for me when I am playing the bass. If I am just listening around and trying to figure something out, I can get confused easily.