I listen to the to the original recording, and try to mentally tune out the bass, or if needed make the EQ favor making the bass hard to hear.
Make sure you can hear the percussionist and draft off of that vibe...
Then I use Transcribe! (music transcription software) to put the recording I have into the right key. Then I just play the song a couple times just hitting roots.
I'll deviate from that if a little 5th, minor 3rd, or octave thing is just plain obvious....
So run through the new song a couple times like that. Then flip focus to paying attention to what the bassist on the recording is doing. If there's something clever going on there that I need to assimilate (that's within my skill set), I'll grab it and add it.
Once I have all that strategy stuff down, just quality check make sure the bass line I'm settling in on is tasteful, respects the other instruments and is supportive of the song.