The main songwriter for Blue Noise Kitchen and Lefty and the Hatman would send out chord grids/charts. No written lines but enough of a road map that I could show up and follow along with him on acoustic guitar, "writing" a bass line as I went. Then we'd work through things over time. What is interesting is that over about 3 years of Blue Noise Kitchen, the gigs went from "acoustic" duo to trio to adding a drummer to adding keys to adding sax. I did some heavy rearrangements of a few tunes from when they first came into the group, but many of the signature bass lines that I came up with early on stuck. I either got it right the first time or got lazy :-D
I've mostly played in original rock bands, and the process was often like this, except the chord charts usually weren't sent in advance. They'd be waiting for me on the music stand at rehearsal. Sometimes, the songwriters wouldn't even provide chord charts. We'd show up at rehearsal, he'd play the progressions telling us the chords, and we'd arrange from there. Also, like nostatic's experience, in my last band, some of the lines I created early on, even during my audition, stuck around for ten years!
In some cases, when the songwriter introduced a track to the band, I'd record him playing the main progressions over and over so I could compose parts at home, or even in the car. I'd create my part singing along with the track, and then figure it out on the fretboard at home. Sometimes I created better parts when I didn't know the chords, because I was less psychologically tethered to the root.
For one band, I was given a recording of their tracks to learn parts for my audition, and our sets were largely drawn from that batch of songs. The chords weren't written out, apart from one track for which I requested a chart. It was mostly learning by ear.
I've also played a few musical theater shows. The first two involved chord charts, and were relatively simple. The other was an amateur production of RENT, which required me to dust off, and then dramatically improve, my standard notation reading. I learned it through a mixture of reading and playing along with the original Broadway cast recording.