How Do I Talk To A Shy Exchange Student?

I'm a freshman in college and there is a girl from Australia in one of my classes. I've only been able to talk to her once, and she was very nice and I even walked her back to her dorm and she said "See you in class" with a smile. That's been about a week ago, and she will smile back at me in class, but I haven't been able to talk to her since. She is really hard to catch after class, and she always seems to be in a hurry. I just want to be friendly is all. She seems to keep to herself mostly, but I'd really like to talk to her. I would like to ask her to dinner, or to show her around town more, but she seems distant. I don't want to stalk her, or come off as a creep, but I like her, and I'd like to get to know her better, and be her friend. How can I approach her without being too intrusive? What is a good way to break the ice?