Search Results: approaching younger women

So the story goes like this. We are both at university in the same group she's 3 years younger than me. Things I noticed:
1) She's not shy around other men
2) Really shy around me
3) She looks at me and if I notice looks to the floor side, blushes, smiles
4) Laughs at my stupid dumb ass jokes ( I did some super lame ones just to see her reaction)
5) Sometimes when I look at her, she notices, I smile at her, she smiles back

Got her phone number over Facebook chat, so she is a really busy student (med. school) and I hate chatrooms, decided to ask her out but when I called asked her what where the plans for the week, that we could go to the sea and have a walk in the evening and enjoy some fresh air. She was like ummm... and after an awkward silence (lasted like 7 sec or smth) changed the topic and asked about the school and I answered and then ended the call.
Lately she's been staring at me across the room like constantly & smiling ( I sneak peak at her with corner of the eye). When I look normally, she freaks out & looks down.
I have talked to her a few times. But the one time that I wanted to ask her out our eyes met and we both where staring at each other for 30 sec or more. There were other people around and this wasn't a party. And I chickened and went away. Does not happen to me usually in these kind of situations.
Ok, so I decided to make a "direct" approach (after a 2 days) over text by saying that I will be waiting her at the train station (near the sea) x and the time y.
She answered the next morning:" I don't want want to go anywhere with you. Please do not get offended at me. "
I was in my head: Ok, that's the end of the game and wrote "Thanks for the open and direct answer"
I think that I was too pushy, too fast and scared away?
P.S We have school holidays now. Still have a crush, I talk a lot with women, not shy and feel comfortable around people in general.