"Something about demons that possess people, and protection from them." she had no desire to have a demon running around inside of her, and apparently there were ways to keep them out of places. If that was the case, then Billie was all for learning it. "I guess we can't just vanquish them. They have to be exorcised, which means learning latin." and probably lots of it. Just wonderful.
Either way she needed to learn how to do these things, so they could both learn them. Of course she would pass on whatever Paige taught her to Christy about keeping herself safe from demons. The others might not trust Christy, and with valid reasons, but it would be worse if she was possessed.
She'd been thinking the same thing, but she also felt the need to tell the sisters the truth. "I was debating that...but I think Wyatt is going to tell them either way." because he would know, and he probably wasn't going to keep the story from Phoebe and Paige if they asked.