You probably don't know what her relationships at home are like. But you have nothing to loose if you do it in the right way.
Tell her having her around has been good and the time went so fast. Ask her if she would mind if you kept in touch. Hopefully she will "Sure, here is my email address." If she doesn't then she isn't interested.
A couple of weeks later at least (but don't leave it too long) send her an email. Just a simple thankyou for coming and that you hope she will be able to come back next year.
This also gives you both a chance to review your impressions of each other before you communicate. Once again if she is interested she will write back.
She might write back and say she enjoyed it and then say something about her boyfriend. But you will never know if you have a chance it you just let her walk away. This way everyone is safe.
Never overplay your hand. If this is going to happen it will with a little encouragement but don't set your heart on it.