A “Walking Bass Line” is a type of bass part playing a specific series of notes on the pulse of the song.
The primary functions of a walking bass line are to outline the chords while supporting the rhythm by playing the pulse of the music. There are many books on the musical specifics, and here is the “bottom line”:
A walking bass line needs to be:
1. Theoretically perfect
2. Musically appropriate
3. Artistically played
Theoretical perfection can start with arpeggios, expanded by adding consecutive scale tones then elaborated with chromatic passing tones. (All of these terms are defined in the glossary at buttwinickmusic.com.)
Musical appropriateness is determined by the style of music, i.e., Broadway, swing, jazz, blues, etc. And the artistic execution is determined by how the musician puts it all together according to his sense of pitch, rhythm and group dynamic.
Trying to be artistic or musically appropriate before having theoretical perfection is a waste of time simply because it can’t be done. Certain styles of music can be “faked” while other styles cannot. (Though I did have a student once who was theoretically illiterate and musical brilliant.)
Walking bass lines are a skill that needs to be developed and nurtured. They are a joy to play and listen to. Ray Brown is probably the God of this, and listening to him play will give you good examples of all three levels mentioned above.