In the women's world, that's what we call taboo. It's like an unspoken rule but everybody knows about it. Even if the girl has already moved on, she can never deny that she still has some feelings for you and with the thought of you and her bessy being together after you guys, it's just not right at all.
But the general "rule", as we all know it, is that it's okay to be with someone as long as they're not committed. In this case, it's quite different since we also need to look at the situation with utmost sensitivity with the friendship between your ex and her bessy.
I think it'll be alright once she gives you her blessings. Give it time. And maybe soon, you can all talk about it and then truly say that everything's gonna be fine. You also have to respect the friendship between the two.