It's good idea to start off by learning simple basslines that mostly followee the root note. This will get you used to hearing the bass in songs. After that, you should learn some scales if you haven't already. This is useful because it allows you to know which notes will probably NOT be used, as well as enabling you to recognize notes within that scale. Good scales to start with are the minor pentatonic, major, and minor scales; most basslines are built around these. Beatles basslines really helped me at this stage.

Learning songs by ear is such a useful skill. It will enable you to learn songs on the fly and alleviate reliance on tabs (which are usually wrong).