The reports of "friendzone" are grossly exaggerated on this site. It really doesn't exist after a certain age, usually after college.
An adult women (ESPECIALLY one with a BF) simply DOES NOT repeatedly hang out one on one with a straight male she just met unless she is attracted to him. Think about: When you see a (straight) man and woman going to the movies together, or shopping together, or even driving together, you ASSUME they are more than friends...and you're usually correct. A woman with a BF that hangs out ALONE with a guy she just met would no doubt raise strong suspicions of infidelity, even if she claimed they were "just friends." Furthermore, anyone who's ever been in the TRUE friendzone can tell you that once they made their intentions known, things got uncomfortable and the girl stopped hanging out with them.
Similarly, if you ask a woman to accompany you on an activity one-on-one, she KNOWS it's a date. You don't need to wonder if "she only likes you as a friend," because she wouldn't be there if she was. The only exception is if a woman constantly brings up a boyfriend or a guy she's seeing--but that's rare. Girls don't keep straight male confidantes.
In your situation, the girl's actions indicate that she is attracted to you, but the BF thing could mean she's just an AW. However, most attractive girls DO have boyfriends, and this one could very likely be on the way out. You need to find this out indirectly by inviting her on a non-threatening group date with your friends. If she has a BF that she is serious about, she will likely not accept, but if she's "testing the waters" and planning on leaving him, she'll find a way to join you. Asking her out one on one is a no-no; it's too obvious, and even if she's attracted to you she will say no (unless she's a cheater, and those are never quality girls). The line about the parties is a good one, but it may be stronger if you actually plan an outing and bring her into YOUR world.