| In a sus4 chord, the third doesn't explictly become a note to avoid - on the contrary, its a very important note in defining the tonality. It does however require special attention. It's not functioning as the third of the chord, rather, its function as a passing tone, or if you want to think of it as part of the chord, tension 10 (yes, its an odd concept, tension 10, but you'll find that as an upper extension of a sus4 chord it doesn't sound too bad). The trick is to play it, but NOT emphasize it. This is very difficult to do, and in most cases doesn't work in things like walking lines for a variety of logistical reasons, which is why people get the impression that you should avoid it. In classical harmony, yes, in pop/jazz harmony, not necessarily.
The trick in walking a bassline over a sus4 chord is to play the 4 on a strong beat (1 or 3) WITHOUT it sounding like the sus4 chord has resolve to the tonic a perfect fourth up. In the key of C, on a G7sus chord going to C major, if you play something like G D C G - just a matter of outlining the sus4 triad, it'll sound weird and prematurely resolved to C. One option, like somebody mentioned, is to play the suspension resolution pattern in your line. This would best, in my opinion, be represented by playing a line like G D C B and then resolving it to C on the next beat. Playing G C B G probably isn't a good idea since the third is on an accented beat.
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