They used to be called leading tones, but that name was wrong, because leading tones only appear below the note they lead to. A better term, as you already know, is approach tone.
Approach tones are any note that leads to a chord tone, either from above or below. They are always within one tone of the note they are approaching. In other words, they are either a whole step or a half step away, in either direction. This is good news for improvisers. As you aim for a chord tone to settle on, it gives you four choices of notes to play right before it. I am not saying all will sound good. Based on the key and the chord, some are better choices than others.
So how do we incorporate variety into our walking bass lines? Well, thinking only in terms of linear lines — not addressing ping pong type basslines, or lines that bounce around willy-nilly — popular thinking says there are three ways to move from chord to chord:
- Like a scale
- Like an arpeggio
- Chromatically
- A hybrid of the above three
So really, four different ways. Add to that, you can walk up or down. This gives you eight or more possibilities to get from one chord to the next. That is a lot of variety. You could play through the changes eight times, and never do it the same way twice.
As already mentioned, some note choices are better than others. How can you know ahead of time which notes will sound better? The answer to that, is
music theory. At the very least, understanding
scales,
keys, and
chords will give you the tools you need to make better decisions than just playing and hoping for the best. Theory allows you to bypass the trial and error phase of figuring out what sounds good.
Good luck in your pursuit of walking perfection. It really is an entire course unto itself.