I'm sorry, but I think you answered your own question. Time will tell. She wants time and space, and unless you give that to her, even friendship won't work.
Some of the best friends don't talk to each other for long periods of time. No one wants someone who is needy, but I get it. I'm needy myself. We all long for that closeness, and some of us, when we get that, get scared. I think she might just be afraid of her own feelings for you. Give it time, try to relax about it, and find something that makes you somewhat happy, something you enjoy to pass the time. If we don't have our own happiness, things we find enjoyable, we can't make others happy ourselves. Just my two cents. Best wishes to you!