How do I mend her heart and be with her again?

I was with my favorite girl ever for almost 2 years, we lived in a 2 family split college house for 9 months (we met when she moved in upstairs). We were really close and she liked me so much. I graduated college and moved into another part of town while she has 2 more years. I began working many hours and work was always on my mind. It didn't make her mad though and she liked me more than ever. I got frustrated with her and found her to be really needy and she would get mad if I didn't call her for a day. I broke it off saying I feel like I am your only source of happiness and you need to be happy on your own. (i'm a jerk) I told her we would be friends. She would call late at night and I didn't answered because I would have to work at 6am. 2 months later I told her how sorry I am. She said she decided we will not be together. Its been 5 months now. We still see each other every other week or so and it tortures me. I think she is flirting with me sometimes, but I don't know anymore. I called her and broke down. I was real shaky asking to make dinner for her. She said I can't expect to do this because it is a boyfriend thing and I can't expect anything to happen. I told her to reconsider her feelings for me, but she said there are no feelings and I never made her happy when we dated. I waited about a month to call her. We got drinks it went great and she said how fun it was and thanks for hanging out with me and sorry i've been so busy to see you. But I fear to bring up questions of us again. I just feel like she still likes me, but I broke her heart and hurt her bad. I want to make it up so much. I figured out work is not everything in life which I have told her. How do I win her back after hurting her so much? Is this possible? and I am a caring person, I just was lost for a few weeks.