I had to learn a whole stack of songs for a black tie, jazz gig a few years back. I’m not a jazz player, but I’ve played in a few blues outfits where I’ve used walking bass lines. When learning the set, I desperately tried to show horn walking lines into everything, only to find that a good proportion of the originals just had a nicely swinging root/V bass line. Once I became away of this, things became easier. Walk where appropriate (underpinning solos is a good place to break them out) but don’t overlook a simpler line that swings, remember that a lot of the original lines would have been played on a double bass and walking everything on a DB is exhausting, so those guys may well have kept it simple, just to be able to do the gig.