Does the TR-09 have a THRU port or an echo function on it's out port? Without that you will not have anything the BSP does being passed to your two synths using the setup you are suggesting. A better solution would be to run the BSP to the splitter then one output going to the TR-09 as well as the two synths.
Is it essential that the TR-09 is the time keeper? Does the TR-09 send MIDI tempo data when not running itself?
You will need to have the TR-09 sending MIDI clock (tempo) to the BSP so that when you change the tempo on the TR-09 that will be reflected on the BSP and then have the BSP send it's notes etc onto the three instruments.
The BSP is a very stable clock these days, but still doesn't send clock when stopped, which can really mess with being it the master clock. In the setup you are entertaining, the TR-09 will be the master clock, but if you want to run the sequencers on the synths while the BSP is stopped, they won't receive any tempo to lock to and won't run. The BSP doesn't have MIDI THRU either, but that won't impact upon what you are wanting to do.
This all makes it sound like the BSP isn't what you want, but that is not the case. MIDI is something which every maker does differently and there is no real standard on how the standard should be implemented. One thing that Roland don't seem to think is important is MIDI THRU. Putting a cheaper Roland device into a MIDI setup usually means it has to sit at the end of a chain, as more often than not they have no THRU port nor do they echo the MIDI they receive in on the output port. Even my super-expensive, top of the line MV-8000 is missing a dedicated THRU port despite the fact it has two MIDI out ports. To send MIDI beyond it, I need to enable MIDI THRU on one (or both) of the out's or employ a MIDI splitter and run a bypass line to continue data down the chain.
I thoroughly endorse the BSP in any MIDI/CV environment. I'm considering a second that's how much I love the things, but to really make the most of one I'd suggest you do a bit of reading about MIDI. Even if you decide not to get a BSP I'd suggest it. Synths and drummachines and samplers and sequencers and fx and recording all revolve around it. Yes there is CV and analogue sync and all that stuff from the 1970's, but even with the three different ideas what should be the MIDI standard, it's still way more streamlined across all companies than CV/Gate is; there is one way to sync MIDI using it's clocking system, not 5 (or more) that exist in the CV/Gate world for a start.
Read your manuals and try doing a MIDI setup with the instruments you own currently. See if you can run the Bass Station 2's sequencer/arpeggiator out via MIDI onto your TB-03 (connect a MIDI cable from the BS2's MIDI out to the TB-03's MIDI in). You will need to make sure the two synths are on the same channel so become familiar with how to change your instrument's MIDI channels. Do the same with the TB-03's sequencer (reverse the connections so that the TB-03's out is running to the BS2's MIDI in). Learn the way those machines send and receive MIDI. For a bit of fun, set your Bass Station to channel 10 (MIDI's standard percussion channel, no matter what MIDI standard your machine adheres to) then send the TR-09 to it and listen to both at once.
