The Smart BP (the one with Bluetooth) is a pretty amazing device.
To do what you need, you will need to set it to "Lithium" mode. This makes is a pretty "dumb" "Smart BP" -- it no longer monitors anything, and becomes a simple switch, immediately doing exactly what it is told. This the mode you want.
If you go to item 10 on page 3, it discusses remote control. The BP can be turned on/off by any of three methods -- pick the one you like.
1) A switch that shorts the H and L pin on the remote.
2) Providing 12V to the H pin (12V makes it conduct, when disconnected it stops conducting)
3) Providing Ground to the L pin (grounded, it conducts, ungrounded it stops). This is what I use on my installation, but I have different configuration than you.
I don't know what the DSSR requires to operate -- but, I'm about 99% sure that one of the three BP modes will work with it!
I'm a bit of a champion of the BP. It's pretty awesome. Cheap, easy, flexible, and does what it says on the tin.