His old best friend hates me?

My boyfriend and this girl were best friends and used to go out together a lot. I think he liked her, but she'd just fallen out with a boy and wasn't ready for a new relationship even though she liked him too.

However, my boyfriend asked me to go out with him one night and we instantly clicked. We became best friends and then entered our relationship. As soon as this girl found out, she blocked me on facebook and deleted him. I didn't even know they were friends so it wasn't my fault at all, if anything it was him who upset her. Me and this girl were friends before but she wont even look at me now. She then added him back on facebook, he ignored her for a while but said he 'accidently' added her and won't delete her now as it seems mean.

He says he never loved her, but just wanted a relationship back then and she was just there. Recently she messaged him calling him 'beautiful.' He responded, not being flirty, but adding kisses. He then deleted all of the conversation.

She asked him to give her a lift somewhere, he agreed to for the fuel money, but he went behind my back because he knew I wouldn't like it.

How do I stand with her? I don't hate her but I hate the fact my bf is friends with her and actually spoke to her. He admits he was wrong for going behind my back and it wasn't the right thing to do. But he lies a lot and I'm scared he will cheat on me. However he did have every opportunity to get with her before.