Break up with him
Girls are often very skeptical of their best friend’s boyfriend when they meet them for the first time. They have to give their opinion on the guy and it will take them a while before they start to warm up to him. Just remember that your girlfriend’s best friend knows everything about you.
She is basically the silent third member of that relationship and you just have to deal with it. But if she doesn’t like you, watch out, because that could add a lot of pressure on your relationship. So do your best to get her on your side, it will help you out in the long run.