She's got a boyfriend...mmm...in that case approach her "as a friend", any excuse will do i.e. offer help with something or ask her to recommend a movie or music or whatever. Get close to her as a friend and take that opportunity to show her why you're a great guy (without being too obvious). If you're lucky, sooner or later her relationship will go thru a rough patch. If the guy is great I'm afraid you don't stand a chance. But if the guy is a jerk, well, she'll be single again soon, which is great news for you!