Look... don't believe all this stuff about girls messing with guys' heads. There are a tiny, tiny percentage of girls that do that, but the rest of us just want a nice guy to ask us out, ok?
Don't "go in for the kill" (she might just be a karate expert) or say something really smarmy and arrogant. Ask her if you can take her number so you guys can carry on chatting through the summer hols. If that goes well, ask her is she wants to meet up. Most girls know what guys are like, so she'll assume, and if she isn't interested, will probably let you down gently.
But go for it, please! I like a guy at my school and am too much of a wimp to do anything: don't be like me.