I'm expecting my best friend to not hang out with my ex
Why do you want her to do that?
I don't want them to get close.
I can understand where you're coming from, I would recommend talking with your friend about this. It wouldn't be good to at this get in between your friendship.
It would just really affect me if that happened and they did get close. I would feel betrayed.
It's okay if you feel betrayed if you still have feelings for them. I recommend you communicate this with your friend.