thank you for your question.
Your girlfriend seems to be saying she needs time and space in order to decide what she wants. Based on the steps she has taken so far, it is doubtful you will get her back in the short term, but you may in the long term.
Your best chance is to respect her for her decision, and honor what she is trying to do.
I can not give you a script to follow, because I do not know her or your personality. However I can make a suggested set of words and phrases, that you can base your own comments on.
YOu might say: Honey, I understand what you are feeling and trying to do. I agree with you and respect that.
If you fight for her, she expects that at some level,and is prepared to fight also for her time and space. So do the unexpected....agree with her. Let her know how you feel about her, but do not "beg" her to change her mind.
Instead, ask her, how you can help?
Do not tell her you will "wait" for her. This is a situation where the more you say may only make it worse for you.
Instead tell her, that you wish her the best and to let you know if she needs anything.
Tell her to please not wait too long, but that if you are still available you might try it again in the future.
The instinct is to fight for her....but that is exactly what you should not do. It would be different if you had done something wrong. BUT, in this instance, you have done nothing wrong. Your only problem is that it is a long distance relationship.
So in this instance, to try to talk her out of it, would be the wrong move. You might ask her: is there anything I can do or say to change your mind? (for example,moving to her home town).