I don't know how many times I have referred to The Art of Seduction already, but here we go again...
First, if a girl is perfectly happy (in love) with her boyfriend, there is no way you will be able to seduce her. She may still enjoy the conversation with you though. The only way to tell is to do your quick version first, ask whether she is interested in a date or whatever you ask them, and take her number. If you get it, you can spend another 10-15 minutes in set to build a deeper connection. Otherwise you can end the conversation immediately.
Second, seduction requires pain. If a girl has a boyfriend, but is not totally happy with her life, you need to poke in the wound so to speak. In a very subtle way (without speaking it out loud) you need to remind her about the things that she is unhappy about, and look like the guy who can give her what she wants.
An example... If she wants to travel but is prevented by her boyfriend for some reason, you can start talking about all the fun plans you have to travel all over the globe with your friends. Avoid inviting her though! She needs to become a bit frustrated and jealous first (the pain that you need for the seduction). After a while, when you have cause enough pain, it's time to invite her. Start small with something "by the way, we are going to X this weekend to do Y. maybe there is room for you too if you are interested? I need to check with my friends though.". Here you give her some hope, but not giving it away for free. Leave her with the comment that "you need to check with your friends first" - leave her in ignorance whether she can join you. If you have done a good job, you don't even need to call her back. She will contact you.