Not a deep answer, but I also play guitar (the third instrument I took up, and my main instrument really). Some songs I’m much more interested in as a guitarist, some I much more interested in as a bassist, and some it’s about equal, so my approach varies.
If I’m mainly interested in it on bass, well, if there’s a signature riff involved or some such, I may start there. If it’s a complicated [to me] riff I’m having trouble with, I’ll probably look up tab. But otherwise, if I’m not starting with a riff, I’ll probably try to figure out the roots first to get the progression down, and then work on making my part more interesting from there. If that’s not working, I’ll look up a chord chart (it probably helps if I’ve already taken at least a bit of a stab at it without a chord chart, and then the chord chart fills in the blanks… if it’s a good/appropriate chart, but that’s kind of another topic. I may end up consulting multiple chord charts for the song and make some adjustments to come up with my own chart). However, sometimes the roots aren’t enough for me to really "get" the song and I end up switching to guitar and the full chords and the guitar rhythm, and this may lead to (Oh no!) singing too, if it’s a song with a vocal
if I’m mainly interested in the song on guitar, the process is pretty much the same except that I’ll start on guitar.
But sometimes I can’t figure out the progression on guitar so I’ll go to bass (or at least the low E and A strings on the guitar) and try to work out the roots first before continuing on.
Once I have the progression down, I’ll typically work on laying it down on a looper, first either on guitar or bass as appropriate, and then the other instrument (whichever I didn’t start with) over that. Then I’ll probably play around with improvising over it, then I’ll probably work on improving my parts and re-recording my loops. At some point, if I’m feeling ambitious (which I haven’t been lately), I’ll work on recording the whole song.
The part that sucks is that I’ve got knee problems that have lead me to give up on drumming, which while not my best instrument, was the most fun instrument for me and which really helped me learn a song in a much fuller way. But anyway, yeah, I often use other instruments, now only guitar really (used to sometimes be piano, but I haven’t been regularly messing with piano in years now), to help me really learn a progression. One could do the chords on bass, but I’m not Mr. Chords on Bass and it’s easier for me to just pick up a guitar (of which, like basses, I have plenty, lol).
So I guess my tips are, learning the roots, deciding on a chord chart I like (including writing the chord chart down myself, possibly modifying it, possibly transposing it, possibly writing it down as Roman Numerals for easier transposition, writing the chords I’ve chosen over the lyrics [if any]), also learning it on a chordal instrument, singing it if there are lyrics, laying down a loop of it, messing around over the loop, formalizing a better part and looping that (perhaps a multi-step process), and then finally either recording the song or jamming it with other musicians (or preferably, both). Compared to what others have shared so far, my unique aspects seem to be incorporation of a looper as a learning tool and also sometimes making a semi-formal recording (probably involving playing multiple instruments), also in part as a learning tool. Introducing it in a jam…
By the way, I’m not claiming I’m great at this or anything, lol. Just sharing what I do
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