Learning music takes discipline. If you use TAB regularly you should become very fluent in reading it. However, TAB along does not contain everything you need to play a song unless it is written with rhythmic notation.I feel like my problem is me not sticking to a song. I can learn alright, but not play a new song on the spot while following the tabs (which is also another problem of mine I believe)
I am not fluent in tab. I can peck my way through it, but I don't tend to use it. I read standard music notation and chord notation. I was normally expected to know cover tunes by memory.
To learn and memorize a cover tune my process is something like this:
1. Listen to the song to become familiar. Figure out the first note and key.
2. Figure out the bass line note for note. I do this by listening to short segments and trying to figure out the rhythm and notes. Sometimes I think in intervals and patterns, and sometimes I think in terms of notes. If the bass line is simple this goes very quickly. If the bassline is technical and fast, learning the part can take considerable time. If it's super difficult I may need to write all or part of the bassline out. Once I get a pretty good handle on the rhythms and notes, it's a matter of knowing where I am and sort of imagining what comes next. Learning to this level requires considerable repetition (dedication).
3. Figure out the form and write it out if necessary. Usually something simple like AABA usually doesn't require a note.
4. Review any notes I have made and practice along with a recording. This is used to learn the song as well as refresh my memory if I am expected to perform a song I haven't played for awhile
At some points in my career I wrote out bass lead sheets. Lead sheets show the melody, form, and chords in standard notation. A bass lead sheet usually only show the form and chords. It can also include sections of the bass line written out out, or cues for vocals or other instruments that are used to help keep my place or know when to start playing.
Some players think by numbers. Numbers are used a representation of the chords and notes. I can sort of understand how this might work, but it's not something I am fluent with. I suspect I may not have certain natural abilities required for this approach. People that are highly fluent tend to have the ability to learn new material very quickly. However it's more like recognizing parts of songs they already have committed to memory. for example, say you are learning a song with form AABA. The A section may consist of chords from two songs you know. The B songs may have the same chords as a third song. Once you figure this out, you can use a memory trick to recall the chords rather than having to learn them. Some people can listen to a song once or twice and have it figured out.