Suspended 4th
Bbsus4 is a suspended chord on Bb. Suspended chords replace the third with a fourth or second, creating an open, ambiguous quality. In jazz, sus chords are often used as dominants that delay resolution (Mulholland & Hojnacki, The Berklee Book of Jazz Harmony).
2 voicings · suspended
Suspended chords are neither major nor minor — the absence of the third creates ambiguity. In functional harmony, 7sus4 chords often appear as V chords that delay the resolution of the fourth to the third (Levine, The Jazz Theory Book). In modal jazz, sus chords can be sustained indefinitely as harmonic centres, as heard in Herbie Hancock's playing with Miles Davis.
Mixolydian mode for 7sus4 chords. The Mixolydian scale with the fourth emphasized rather than the third reflects the chord's suspended quality (Aebersold, Jazz Handbook).
Suspended chords resolve by moving the 4th down to the 3rd, converting to a regular major or dominant chord.
Sus resolution
Bbsus4 resolving to a regular dominant or major chord
Modal jazz
Sus chords sustained as modal centres
Bbsus4 replaces the third with a perfect fourth (sus4) or major second (sus2), creating an open, neither-major-nor-minor sound (Levine, The Jazz Theory Book).
Sus chords in jazz function differently from classical suspensions — they can stand on their own as harmonic entities rather than always resolving.
— Mulholland & Hojnacki, The Berklee Book of Jazz Harmony