How do I deal with my girlfriends mood swings?

(I never thought I will ask this here. sighhh!! Here goes.)

Hi.

She is my first girlfriend and I love her very much, and wants to see her or hear from her at least once in a day if circumstance allows us. I believe it is very normal of a young man to feel this way towards the girl he loves. We have been seeing each other only for 3 months. I know how busy our lives can be, but I have LOTS of free time, and I am always ready to see her if she's available. I like to plan things ahead, but I never know when my girl friend would want to see me. I would send her many texts, calls, emails. I would ask her out on dates, movies, dinners, hangouts, little questions to know her, ...But she would ignore all of them. Then once a week she would see me. She would spontaneously decide to see me and I get to see her by surprise out of no where. She would hug me, or kiss me, hold hands with me. But by this point I am terribly hurt, confused and have been feeling lonely, have all these questions in my mind. And I always tell her carefully not trying to spoil the little time she gives us, how much I missed her, and how much I deserve at least a reply to my texts, a call back or an email. She would say she's sorry, after some disagreement, discussion and new promises we would have good time together few hours (usually me taking all the initiatives because she never does. sigh!), and before we leave I would tell her again how our important this is to me, give 'us' more time together to know, to take initiatives and see each other in our lives, and to please let me see her again (often times imploring) and then the cycle repeats.... Another 4 to 5 days of complete silence ?!??

Each time she does it to me, it breaks trust. I would have no idea when to see or hear from her until she decides when?? Which hurts so much. And I feel she doesn't want me. But at least tell me so. Its like she's keeps me in hopes, waiting, desire,.... and she seems me whenever she needs me. I hate to say this, but I feel being used. I feel stretched and pulled between her. Relationships are not supposed to be this way this early. It should be fun filled, and always excited for each other, and getting to know each other. But not for her. She's either uncommunicative, sad or happy. And I am dying in confusion, hurts and loneliness. Its not like I haven't told her about this. I have many times. Everytime. Communication is important to me. I have told her that she can always talk to me about anything. She trusts me. And I trust her. But each time she' does this to me, its breaking that trust. There is an invisible bubble that is slowly developing in her, and I hopefully wait. I am always transparent and open to her. She knows everything about me, and I hardly know her?!?

The interesting this is she is the one who found me, and wanted me so dearly. She is very attracted to me and she's the one who pursued me, texting, calling, letters. I wasn't trying to play hard to get or anything, I always wanted a relationship all my life, its just that it takes time for me to trust a person, and I warmed up to her rather slowly, but once I did, which happened in few weeks, and now I need her most, I love her, I need her lots and I am both actively and genuinely pursuing this relationship. I wish she would remain in my life forever.

But 4-5 days of silences and seeing once a week (if I am lucky), her complete ignorance of my questions, being insensitive to my feelings, is driving me insane. She won't even say sorry after days of silence. Its always as if nothing happened???

What do I do? How do I deal with her mood swings? How can I be a good friend to her? (Sorry this was long, but I felt I had to explain in detail to avoid any confusions.) Thank you for your answers.

(We have both just recently graduated the same college, we are both well and highly educated, have lots of common friends, lots of understanding, compassion, grace and kindness. We are healthy and are not under any medication at least that I am aware of. We both have good morals, character and nature. I am not trying to get in her pants. And we both strongly believe in sex only after marriage.)