hmm you sound young. Girls like confidence, if you don't ask because too afraid or shy with others around, it will turn out bad. Here are some easy options.
1. When you are next to her, get into a conversation with just her. Her friends can be around and talking but it's just both of you talking. Bring up something about an upcoming movie you want to see, or some fun activity, and if she seems interested as well, then casually ask her if she wants to go to it with you. (but it seems you don't have her phone/facebook/email/etc yet and since you seem a bit shy, it might be hard for you to get that 'after' that point which brings #2 option...)
2. Facebook, instagram, snapshot, etc, tons of excuses to get her phone number or contact info where you can then text/email/etc. You can casually ask over that too if you really have a problem asking in person.