BB and BJJ won't work together and trying to make it work will increase your chances of getting injured.
I trained BJJ and Muay Thai, along with lifting for about 5 years. Strength training is very compatible with BJJ, as well endurance training. But if you are truly doing more BB type workouts with body parts being hit several times a week, isolation work, and diet prep, that is not going to work well- especially on ligaments and joints. BJJ is hard enough on the joints to begin with and I ended up dropping it all together.