A little David D tip, dont ask if she has a boyfriend in that way!
Say instead "are you single?"
"Do you have a boyfriend?" just sounds too needy/approval seeking. It also gets asked of her many times. "Are you single?" is far more rare and thus less prone to autopilot responses.
Besides, this information seeking approach is poor to begin with.
And then you introduce yourself, which is comfort building. You are "the next guy".
So by telling your name and asking for hers you are not only classifying yourself as "the next guy", you are also giving two indicators of interest at the open - asking her name and asking if she has a bf, which is also bad because it eliminates the chance for her to give you IOIs.
Like when a girl asks your name, thats an indicator of interest. If you give it up as your opener you eliminate the possibility of her asking for it.
This approach is likely to generate a lot of flakes. Even those who say "sure" will probably not show up. Why? Because you have nothing to talk about, she has no idea who you are, and that would create an uncomfortable situation for her since she doesnt know if she can get along with you.
If you deliver those lines with a different type of body language, you may help eliminate the comfort-building next-guy/nice-guy problem, but then you'd be opening with seduction, which is also bad because if she doesnt like you based on your looks at that moment you get blown out. It gives you no opportunity to convey your personality or get her attraction mechanism going.
Smooth Player, you don't have to do the Mystery Method every time.
You can go with David DeAngelo's line, where he has a way of asking a girl if she's single and getting her # or e-mail without coming off as AFC (go through his Double Your Dating DVD to learn how to do that!).
You can also do his 5 minute number/e-mail technique, where he says "hey, [opener]" and followed by "I gotta get back to my friends, nice talking to you", then you turn away, turn back and say "hey, do you have e-mail?"
Or even his few second technique where you just roll up and say "hey I'd love to meet you, but I gotta go, do you have e-mail?". That's even shorter than your current interview-style interaction as it requires only 1 line. Since its so short and there is so little that can go in any unpredictable direction you can rehearse it good.
But once you get the number or e-mail that way, you have to interact a little bit through that (a few e-mails back and forth or maybe a few brief phone calls) so that you can build enough comfort for her to want to meet you.
In the case of using the mystery method, or any sort of prolonged scenario where you have a chance to speak for maybe 10-15 minutes and build enough comfort during the approach for a meet, use a time bridge like "hey, I am going to go check out the new book at the bookstore, you should come with"
Otherwise, if not enough comfort was built, like if you had under 2 minutes to meet her I would go with David DeAngelo's idea of interacting briefly through e-mail and/or phone before you ask out.
But unfortunately, Smooth is right . . . That approach is pretty awful. Ok it's worse, but I'm trying to be nice. You could pick apart the opener with MM by thinking that coming right out with your name, you're robbing yourself of a possible IOI (by her asking what your name is during the interaction, once you've reached the hook point). Second, who cares about the boyfriend? "Boyfriend" should only be brought up if she does, and then it should be dealt with accordingly. Third, if you get a number you can count on it being a fake one. What HB is going to give her number out to a guy she's known for 5 seconds? Rapport, dammit, rapport . . . THEN you can go for the number.