The bass part of the BK-9 rhythms will normally play the "root" or "fundamental" of the chord you are currently playing. For example, if you are playing a C chord in any inversion (C, E and G) or (E, G and C) or (G, C and E) the bass part will play a C.
If you press the BASS INV button so it is lit, the bass part will behave differently.
Now, if you play a C chord inversion such as (E, G and C) the bass part will play an E. If you play a C chord inversion such as (G, C and E) the bass part will play a G.
So the BASS INV function gives you creative control over what notes the bass part is going to play.