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If she mentions a BF in the first moments it could be a BS defence mechanism.
I stupidly used to ask chicks if they had a boyfriend, as a way of asking permission to persue them - total AFC!
Then again, if you know the chick is into you, it's just another way of showing her that your into her. I don't think asking this question is going to stale the deal...even though it could imply that your suspicious that she may be about to cheat on someone.
a girl asked me this question, convo went
her; "your hot"
me; "your hot too" (probably could have said something better here)
her; "dyou have a girlfriend?"
me; "no, dyou've a boyfriend?" (what else could I have said after that lead up!?)
her; "no" ... kisses me on cheek "I'll see you later?"

The problem with your bottom conversation is there is no Push/Pull. You pretty much told her she can have you at will. You have to play hard to get son or you're going to be stomped on.
a girl asked me this question, convo went
her; "your hot"
me; i know, thanks for noticing..lol (saying this funny)
her; "dyou have a girlfriend?"
me; "whoa..whoa baby. We just met, and now you are already getting personal this fast? (again, say it in a funny way)
She'll respond to your push/pull.
I can't tell you how many fucking girls I've had come up to me, and tell me I'm cute, I play along, and they end up flaking like a mother fucker. Trust me. Don't go along with the bullshit. Act alpha, what you did is still AFC.