How can I show this girl I love her?

So about a week ago my girlfriend broke up with me. Her main reason being that she had lost feeling for me. She hadn't talked about it for a month and one day gave me a call and told me that she thought it'd be best if we broke up. I told her that I wanted another chance that I still loved her and that she should have told me she felt that way and that we could have worked through it. At any rate I'm in the friend zone now and I'm trying to give her time to think and to choose for herself if she wants to try being in a relationship again. I've already made her feel guilty enough about dumping me so I don't want to plead with her to take me back, I want her to want me back. Is there any way for me to get her feelings for me back without seeming like a possessive ex boyfriend? Do I just act like her friend until she values affection and relationships again? I told her that I'd wait for her and that I hoped she would give us another chance. Even as friends she never messages me first, she only sends replies like she is avoiding me. I'm not a controlling or a bad guy; why would she end it over "not loving me anymore" so out of the blue?
She's just so cold and I don't know where to go from here so I've just messaged her friendly stuff every day or so.
I've thought maybe I could improve myself, I don't know work out more, make more money. I just hope she'll regret dumping me at some point and want me back, because I still love her.
How can I show this girl I love her?
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