There shouldn't be any problem if you switch from Tea Tree OIl from BP, especially since they are both used topically, so they really shouldn't interact at all (so long as you don't put them on at the same time). 

You probably will experience a shift in how your skin reacts to BP compared to TTO, though. While TTO can be pretty irritating to the skin, BP can be even more irritating depending on the % of BP in the product you decide to use and the amount/frequency that you use it. However, this can be easily mitigated by using a noncomedogenic moisturizer as well as paying close attention to how your skin reacts to the BP.

While using BP, make sure to start off using low amounts off it in order to see how your skin will react with it. A little irritation at first is to be expected, as it is very drying. Continue to increase the amount that you use until you start noticing an effect, but definitely go push it too far or you will have skin that nearly resembles a burn (trust me, i've been there  ).

On a final note, you can use BP twice a day, and I hope you find great success with this product!