Adding passing tones and neighboring tones allows the bassist to make things more linear. You'll still want to emphasize chord tones on strong beats (the first and third beats of each bar, in 4/4; the first beat in 3/4).This example contains examples of upper neighbor tones (UNT)-- notes above the chord tone -- lower neighbor tones (LNT) -- notes below the chord tone -- and passing tones (PT)-- notes between chord tones.
Generally speaking, upper neighbor tones should be diatonic (in this case, within the G scale), and lower neighbor tones should be chromatic -- a half step below the note you're returning to. Passing tones are usually diatonic, but can be chromatic; taste comes into play. Measure 6 of this example includes such a passing tone -- the Ab that leads to the root (G) of the next measure.
Too much chromaticism --too many notes outside the key -- weakens the tonality and makes it harder for soloists to hear the progression. It also limits their soloing by giving them less of a harmonic background to play either "with" (in the key) or "against" (chromatically).
