I wouldn't recommend this, I'd use one or the other - or if you're very careful use each on a specific part of your face.
You should call/talk to your derm to see what they say.

First of all, like Geeking said talk to your dermatologist.

I currently use Clindamycin and Differin, the former in the morning and the latter at night. In your case, I'd use clindamycin in the morning and BP at night.

However, keep in mind that BP won't cure your acne, it is simply a band aid treatment. It should only be used imo for spot treatments.