Can you change a homebody?

Me and my best friend are like oil and water. And one of the biggest differences between us is that I am very outgoing and she is a major homebody. Whenever I ask her to do something different or just go out she claims she'd never do it if she hasnt met me. She is a gorgeous girl but wants to spend practically all her time home doing eighter nothing or watching tv or staring at a computer screen. We are both in college and its ridiculous to watch someone close to me spend their life watching everybody else's lives. I wish she could let go more and be more open to new things. Lately if we are together all we do is sit home . Its boring and its time for a change. I'm thinking about just letting her be and spending my time with more outgoing people. Have you ever been in a similar situation? What can I do to show her that life is brighter outside the box?