We are complete rookies in polyamory (though not to non-monogamy), but wanted to hopefully add something of use to you...
I know lying is hard. Not wanting to lie is very admirable. It is very, very difficult, stressful, and damaging to carry around a lie. I know there's perceived rewards of not having to lie to your family anymore should you come out to them. But consider; what do you stand to lose by telling them? What does BB stand to lose? It's possible (I don't know your families) you and he could be effectively shunned from both nuclear families and extended families.
Sometimes when you are telling someone something you are shifting the stress and burden of it from you to them. While it frees you, and you feel a sense of relief, the person with whom you are sharing your concern may feel an enormous weight come down on them.
If, say, you tell your mom; then she has a potential burden. Does shoe tell other nuclear family members? If she doesn't, is she now lying too? What about extended family? Does she now have to keep it all secret and carry that burden now too?
Tread carefully. There is much to consider here.