That's what I thought.. but then how come there's no Ab note in the key of Bb major?
The question isn't really relevant. Your composition is not in Bb major. If it was, the chord would be F7sus..
All major scales are constructed on the same set of relationships between scale tones, theres no Ab in Bb major because it simply doesnt belong.
Just like Ab doesnt belong in Bb major. Neither does your whole chord. in the key of Eb you have 7 basic chords, they are as follows..
Eb major, F minor, G minor, Ab major, Bb major, C minor and D half diminished.
your chord functions as an extension of the 5th or Dominant chord, Bb major.