I know it is difficult because you care for her and want more with her, but it doesn't sound like she shares these same feelings. She may feel friendship for you but not the next level of physical connection or have the desire to be in a relationship. If she wants to spend time as friends with you and that works for you then do that and it is possible that she could develop more feelings, but keep in mind that she began backing away from anything more serious rather quickly after meeting. So, while I understand you feel strongly for her, she might not share that feeling. Hard to hear, I know, but at this point let things play out and see where it goes. Nothing can be forced so if she doesn't have an interest, respecting her feelings is a must.