I think bassists are often warned that they should never play the M3 on a sus chord — probably by their teacher, or a piano player who doesn't want the bassist causing harmonic trouble. It's true that often the lower notes in a sus chord will be the root, 4th, b7. Often in modal jazz, the pianist or guitarist will have the 3rd voiced on top of a sus chord. Check out Herbie Hancock on the original
"Maiden Voyage," where he uses a lot of variations of the Amin7/D or Dsus with an F# on top. Check out Don Kasper's sus chord voicings that he wrote out for us.
As bassists, we don't have a lot to do with that part of the chord, but it's there.
I think confusion arises because a sus chord in functional harmony is often just a substitute for the V7 chord. So instead of having Dmin7, G7, CMaj7 . . . we might see Gsus, CMaj7. Or F/G or Dmin7/G. Those chords are functional within a key signature and are moving, not static. They probably wouldn't have a 3rd in the voicing.
Don also posted an excellent example of modal playing from Alan Pasqua with Jimmy Haslip on bass.
Here is a nice example of the Major 3rd in the melody in a D9sus,13 chord - @ 0:33.
Haslip is playing great, and just holding down the bottom with a bass line something like: D, A, C, D. No 4th, no 3rd. Pasqua (which my auto-correct keeps wanting to change to "pasta") is playing chord voicings from the complete D Mixolydian palette. The melody starts on the note G, but moves through all of the notes of the D Mixolydian. There are two other chord/scales that they use in the tune, but let's leave those for now. When the solos build up, they all sometimes shift out of the D Mixolydian sound, and then go back in (playing outside).
For a more complex use of sus chords, listen to
"Nerfertiti" (1968) with Miles Davis, Wayne Shorter, Herbie Hancock, Ron Carter & Tony Williams. Nefertiti and Maiden Voyage are just as important in the development of modern jazz and modal playing as the "Kind of Blue" album that's been mentioned here a couple of times.
Herbie says the second chord in "Nefertiti" is an Absus sound, but more precisely Ab7(9)sus4Omit5th. Note the sus in the left hand, and the 3rd in the right (in the melody also). Jaco loved to play this tune, btw.
Wayne Shorter wrote the tune, and many other Miles tunes from that era. Word has it that he didn't use chord symbols, and preferred to write out the voicings that he wanted to hear. John Patitucci confirmed that with me, saying that Wayne writes out scores for everyone . . . they aren't just improvising from lead sheets with changes.
My last little point here is that a lot of fake books have the wrong changes for Nefertiti. Especially that second chord. On the original recording, Ron Carter often goes to a Db in the 2nd bar . . . I guess that's his way of saying "I can do sus too!" People transcribed the chord, assuming Ron was playing the root, and I often see it written as Dbsus. The power of the bass 
I think a lot of the confusion, to reiterate my point above, comes from the use of sus chords in modal jazz, and the use of sus chords in functional harmony.
So, don't get bent out of shape . . . @Deacon Blues could sue us, if he wanted
*kidding*
@Fergie Fulton — I've done lots of workshops in GB and Ireland, and I always feel totally tongue-tied when I'm talking music . . . I can't tell my quavers from my crotchet!