How can I get this antisocial girl to warm up? Should I even try?

At my university there's this girl who I always see walking around alone (in the canteen, in the town centre, etc). In the three years I've been there, I've never once seen her to speak to ANYBODY. It's weird because she's cute. A few months back I thought about going up to her and talking to her, but I didn't want to just stop her in town, so I put her out of my mind and went home. Yesterday, though, I was with some girl friends in the canteen when she came in and sat two tables behind us. I figured it was as good an opporunity as any, so I worked up the courage to go speak to her. I sat down on the opposite end of her table and basically said, "Hey, what's up? I see you around often but I've never seen you speak to anyone, bla bla."

She sort of stiffened up and looked uncomfortable. I'm not sure why, because I was careful to not be imposing -- I'm good at making friends and I know how to adjust my behaviour depending on the situation/a stranger's personality. She said something really quietly, I can't remember but it made me certain she wanted me to go away. I thought she might be worried that I was going to ask for her number or something, so I jokily said that she didn't need to worry, I wasn't hitting on her and I just wanted to say hi. She said, again really quietly, "I just want to eat my lunch." I took the hint and said that I'd see her around, and then I said my name and asked her hers. She told me, so I said bye and went back to eating/chatting with my friends.

I can kind of guess why she's always on her own now -- I doubt its because people haven't tried to talk to her. I'm pretty glad that nobody could hear our conversation, because otherwise having to go away so quickly would have been embarassing. But it just makes me want to get her to warm up to me more! What do you think I should do?