This is a question I used to have as well. The answer is I don't use voice leading. Building a walking bass line is more of a melodic process than harmonic...I consider voice leading to be harmonic.
When I was first learning to walk I slowed down and took the music out of time. The idea was to actually think about the appropriate scale and chord tones that might fit and experimented to learn what would work. Over time you build up a vocabulary that works over basic diatonic harmony and play intuitively. I.E. you don't really need to think so much. You see a chord and simply play a line from your vocabulary. You should eventually develop the ability to simultaneously hear the line in your head while you are playing it.
However, in truth I move in and out of different mental processes while reading/interpreting a lead sheet. In one section I may play mostly by ear, and a few bars later I may be think more about the specific chord tones I want to hit...so I am using more of theory-based mindset. Another mental process is to use something called box patterns. the idea is you know and can easily play the shape of common chords in various inversions based on physical finger patterns or shapes...so you don't necessarily need to think in terms of chord tones. This can be really handy when working in a key that you don't know as well as you should.
If the harmony is altered, it gets a bit more tricky, but the process is the same. Slow down and figure it out. Jazz often uses chords that are non-functional, meaning the don't relate to the key center. These chords can be interpreted a variety of ways...the chords outline to chord tones, and interpretation involves deciding which none chord tones to use...or what scale or mode you will play over the chord. The basic chord, notated extensions with alterations, and written melody often inform your choice.
When it comes to building basic walking lines, the general rule is start the bar (beat 1) on the root of the chord. Of course this is a rule you break from time to time as you get more advanced. Beats 1 and 3 receive harmonic emphasis so they should generally be fairly consonant chord tones (1,3,5). Put non chord tones or the 7th on beats 2 and 4.
Generally you limit the size of note to note intervals to under one octave. This is another rule that can be occasionally broken. If you to play the root and 3rd, you can go up a 3rd or down a 6th. However, IMHO the direction and shape of a walking bass line is governed more by rules of melody and counterpoint than voice leading. IMHO these are rules you learn largely by listening to/copying great bass players.
I think of bass lines as either arpeggiated, linear, or hybrid. Arpeggiated is primarily chord tones. Linear is more step wise movement and includes non-chord tones. Hybrid is a mix of both. Most people seem to think that a linear bass line is better/more interesting, however, some songs feature primarily an arpeggiated bass line. I often tend to meander back and between arpeggiated and linear lines. Whether I favor arpeggiated or linear more depends upon what I think works best with a particular song.
There are also various strategies to play non-chord tones that are not linear. This includes tones that are not even in the same key center. After you get comfortable building arpeggiated and linear lines, I suggest learning some of these strategies. Here is a link to an online book:
[Bob magnusson] the_art_of_walking_bass_a_method_(book_za.org) (slideshare.net) This book covers multiple strategies for using non-chord tones...more advanced strategies include the harmonic approach and the chromatic surround, which both employ non-diatonic tones.
