Can I win her friendship back?

My friend and I got into a fight and ended our relationship for a yr. she said we could be the best ever but she was with her bf (ex currently). This made me mad and was why we ended it. However, just recently we met for coffee exactly one month ago. She said she wanted to see me again, but has been busy this past month or was lying. I texted her, " do you want to see me again? I'm sorry how I ruined everything and it would a lot to be your friend again." She didn't respond.. later that night I asked, " do you want to bang? You said it could be the best" Bc 1. She said we could be the best ever 2. I had nothing to lose bc she isn't responding and I never asked her that before. ... I let that stand for the night and texted her the next day, " I'm sorry about those texts last night. I don't want to date or have sex with you, you mean more to me then sex could offer. I just want to be your friend like old times. I'm truly sorry about everything." I really really care for this girl. Being her friend again would make me so happy! I'm not going to text or communicate for two weeks and then try again. Is there anything I can do to show her how much she means to me? I don't want to lose her. ln all honesty, her friendship means more to me then sex could ever give. Is there a chance I can win her back? I think she just needs some time or I should let it go.