I come from a self-taughting background, so I'm sorry for any bad terminology in the question.
Some time ago, when learning Blind Willie Johnson - Nobody's fault but mine, I first practiced the slide guitar melody (the sharp notes). Once I had it down, it was time to add the bass line, which was simply alternating between octaves (6th and 4th open strings) on every beat.
Even with its simplicity, it was really hard to add the bass line because some of the notes would land between rests or in some "odd" places, like the melody wasn't completely in sync with the bass (which is probably one of the things that makes it sounds so nice). I ended up slowly figuring out where the bass notes were and after some practice I could get it. It felt like almost relearning the song, except I had practiced the slides already. I'd find out that there was a bass note somewhere, and would either change the pluck to include it or play it alone in the rests.
I was just worried that this approach is actually keeping me from creating some independence between my bass and melody in other songs, requiring me to do this whole process every time I have to learn a song with an "odd" bass line. I just imagine it's very hard to create independence between the thumb and the other fingers, since the plucking style kind of changes if you have to use the thumb at the same time or not (meaning they are not entirely separated).
Should I keep adding the bass lines that way? If not, what could I do to begin creating independence between the thumb and the other fingers? After that, will it feel natural to add bass lines to other songs?