The 'A' Section
The "A" section chord progression is based on this diatonic progression: I-vi-ii-V7. The remainder of the "A" section progression (the only part that is not I-vi-ii-V7) is IM7-I7-IV7-#IVdim7.
The good news about this is that you can play in the home key over most of these chords. (if you are playing in Bb, you can use the Bb scale over these chords).
You can also use Bb minor pentatonic, if you are so inclined.
the chords that don't work very well with Bb major (IM7-I7-IVM7-#IVdim7) uses the Eb scale.
Keep in mind that the last 8 bars of the song are the same as the first 8.