Why not approach the issue like any other health issue? That's really what it is. Yes, she's an adult, she's going to make her own decisions so you don't want to be too pushy. But as far as I can tell family members do often offer health related advice. I'm 24 and have acid reflux problems and my parents continually tell me in a stern voice "you need to go to a specialist." Of course, I can choose to ignore them and they aren't going to get too upset about it and they will hold their tongues, but just because I'm an adult doesn't mean they can't advise me (even sternly) to do what is in my best interest in terms of my health.
Plus, though she is an adult, isn't it your health insurance which would pay for the prescription? If so, you should probably make known that she should feel free to get it filled using your insurance. Many young women face the problem of trying to figure out how to get the birth control without their parents finding out about it which often means not going through their insurance (though I'm not sure how you would end up finding out whether or not the insurance was used). It probably wouldn't be too hard to do this, but why not simply let her know she needn't go through the trouble?
Other than that, what you do or do not say to her probably depends on the kind of person she is. What is her opinion of premarital sex or casual sex? Might she have already have had sex? What is her attitude towards/experience with alcohol and how might the availability of alcohol at college influence her judgment when it comes to sex? Do you think she could get seriously hurt emotionally if she made a bad choice regarding when to have sex?
When I was a young teen my parents gave me a few vague messages about sex--about birth control, got me the hepatitis vaccine--but I always made a point of knowing a lot about sexuality and reproduction...much more than they knew. So they really didn't need to tell me much. Also my mother once tried to do the "girl thinking" thing some have mentioned. She said something about a cousin of mine who, as a teen, had begun having sex with a boyfriend and then found all he wanted to do was have sex and she was sorry she had ever had sex with him. The message being something like--girls only do it because they want to make boys happy, but boys will just want more and more, so you'd better just never give it to them in the first place. Of course, this ignores the possibility that girls might actually want to have pleasure themselves and might want it just as much as boys. Her doing this just ticked me off--guess I was a girl who's a boy thinker when it comes to sex.
In any case, if it makes you uncomfortable my advice is to at least say something quickly about you supporting her getting the bc pill prescription filled if she wants, and maybe something about condoms, and then leave it at that. After all, emotional scars heal but babies and some STDs are forever.