I'm also a bassist that does a lot of improvisation on stage. I often play with a singer that knows literally thousands of songs, and he often pulls one on me

I'm also a bassist that does a lot of improvisation on stage. I often play with a singer that knows literally thousands of songs, and he often pulls one on me that I've never heard. What matters a lot is genre conventions. This particular singer mostly plays rock, blues, country and reggae. I know the basic mechanics of those four genres, and can often guess where the song is going, even if I've never heard it. Even if I hit a wrong note, it's usually in the chord that's being played (e.g. the 5), and sounds reasonable. I do the same thing when I get a setlist and just listen to the songs multiple times in the days previous so that I can hear the songs in my head. If often say, "If I can sing the melody, I can play it." Per the topic at hand, what's also interesting is that I can think that I don't remember a song, but often even years later, if someone starts playing it, I know immediately where to go. Once I find the key, which rarely takes me more than a note or two, I'm good. But I've also got friends that play traditional Irish music. I can't sit in with them (I've tried) since the chord changes fall at places I don't expect them, and are often different chords than I'd guess. Having a feel for the style of music makes a ginormous difference.