Salud!
I listen and sketch on paper the structure/harmony in 1-2 passes. Like marking "I Love My Dog - G" and then just jotting: V1 (verse1): 1 3 4 4m, 6M etc. (I just mark "accidentals" when they contradict the usual 1M 2m 3m 4M 5M 6m 7M). When harmony goes beyond usual pop/rock simplicity, I write actual chords instead and leave the harmony analysis for later, so I understand what I'm playing.
Then, bass in hand, I make a rhythm note of the basic groove and identify signature/strange parts. Work specifically on them for a few minutes to find the best fingerings in the context.
On to another song.
Then play all the new songs one after the other, repeat, repeat, repeat, repeat...
Edit: When the bassline is a busy one, I usually search bass covers in YouTube, GREAT resource. I've just started using MoisesIA to isolate bass parts, very useful too. In these two cases, I think it's important to understand it *usually* makes no sense to play note for note. More times than not, the bass player surely played improvising small variations over a basic groove/structure. Sometimes, those nuances can be important, as in uber-known Beatles songs, depends on the case. First I get a functional, accurate bass part, then you can refine it with "random" details.