She moved out so you have to give her the time and space to miss you. That's the only way this is going to turn around.
Right now she knows she can get you back anytime she wants so right now you are plan B.
You contact her and ask her to dinner that only reinforces that you are plan B.
Your goal right now is to become her plan A. The best way to become plan A is to start leading an awesome life that she will want to be a part of in the future.