There's many ways to create a left hand walking bass line.  Here's a relatively simple one that I find effective.  On beat 1, play the root.  On beat 2, move either up or down to play the fifth.  On beat 3, play the root.  On beat 4, play the note that is one-half step above or below the next root.  Using "Fly Me to The  Moon" as a sample, you'll see that in the key of "C", that the first four chords are Am7-Dm7-G7-C.  So, you can play A on beat 1, E on beat 2, A on beat 3 and then either Eflat or Dflat on beat 4.  For some inexplicable reason, I have gotten  into the habit of almost always approaching the next chord from a half-step above.  i should practice this device getting comfortable approaching the next root from below as well.  

Nice, Richard... here is your strategy illustrated  .