My boyfriend has a best friend that is a girl. They talk all the time on the phone. Is that normal?

Don't worry about it. I have a best friend that is a girl and there is nothing wrong with it, if she does not like you, tough sh** he does and that's what matters is it not.

Just think about it from his point of view. What if you had a best friend that was a guy? That's what I do to keep myself it check and it has worked so far.

I have a lot of male friends and have always been the girl who gets to hang out with the group of them, even when they have girlfriends. I think its pretty normal. Ironically, from my experience it is the girlfriends who feel threatened by the fact I'm really close to their boyfriends. So maybe she is just worried about you not liking her!
also, this is probably not likely but she might be kinda jealous of you. Even if she's not actually attracted to your boy friend, if they used to spend a lot of time together and he starts ditching her to hang out with you, she is going to feel like she lost her best friend. Make sure your boyfriend has time to hang out with his friends/family and everyone will probably like you better for it.