How to get my girlfriend to open up?

Okay, so me and this girl have been dating for just over two months. We live on a college campus in a special program, and due to the cirstances of this program, we live in the same dorm, but aren't allowed on each others' wings. She is a very shy girl, usually spending the vast majority of her time in her room. It is difficult for me just to get her to leave her room and go to dinner or such. Also, due to her shyness, she is extremely conservative about PDA. Most nights I'll get a hug and a peck on the cheek. If absolutely no one is around, she'll give me a little peck on the lips. Whenever I offer to go on a walk, or to a lookout, she always turns me down. Also, conversation is getting boring and repetitive. I have complimented her, been special to her, wrote her poems. Any advice would be helpful...