Watch the Ostenat-Oh, Yeah! online guitar lesson by Brad Carlton from Chord Studies: Slash Chords Vol. 2
This is a Latin style groove where the bass is going in a root - 5th - octave pattern. Notice how in the first two chords we've got a descending melody; this will continue as we play both the G/C and the B♭/C. Also notice also how your third finger has been a guide throughout. Move down a half-step to get your Fm, then come back down and you'll be on the same fingering that we started out with. Hyperextend the third finger, then come up for the D/C.