Understanding and playing walking bass is not difficult. In fact it can pretty well be formulated.
Here we're guitar players although, of course, the bass is tuned the same way. Also, understanding how to create these bass lines can be an aid to better chord melody playing.
Here are the first few bars of another standard. Again, I'm only putting in guide tones for the melody. It's quite a good example because it has a major 6-2-5-1-4 followed by its minor ii-V-i.