Hi,
I just bought both yesterday. My setup is connecting BSP and KS to the computer with ableton live. Clock goes from ableton live to both devices. Using ableton, I route the midi out from the KS to the midi in of the BSP. This is pretty much equivalent to what you want to achieve. To complete the description, midi out from the BSP goes into ableton and pilots the ableton drum rack (on midi channel 10) and volca bass (on midi channel 2) and waldorf rocket (on midi channel 1). Output of the hw synths goes into my 16 channel audio card, and through ableton those audio signals are routed to the output of the sound card.
My idea was to play the bass and lead lines with the key of the KS instead of the pads of the BSP.
Let me tell you that is quite fiddly, due to the fact that the BSP sequencers are mono. You have to press the MUTE button on the BSP to hear the sound while you're playing (for example the drum part).
The KS sends out the arpeggiator notes on the midi out, so those are fed to the BSP. It's more the problem that the sequencer on the BSP has a resolution, and let's say if you play the arpeggiator with 1/32th and the sequencer on the BSP is set to 1/16th, i don't think it will store 2 notes for each step.
Today i didn't do enough tries to answer you properly, cause i used the hw synths and one has an arpeggiator too, so big mess.
Overall, after i discovered the MUTE button thing on the BSP, for me it worked with simple basslines (1 bar notes) and with the arpeggiator (?!) (in the sense that out of the mess coming out from hw synth you could hear some kind of repeated notes :DDDD ).
If you are still interested i can keep you posted.