Interesting idea. Now I have never bought a stranger a drink, so my reaction is purely hypothetical. I think the idea behind buying a girl a drink is that she now owes you a conversation. Basically, you're trying to buy her time and attention, which is strange since your time and attention should be equally if not more valuable. Nonetheless, I wouldn't make a promise and then immediately back out, because what kind of first impression does that make? But buying her a drink does skew the balance of power, which I believe undesirable. What I would do to fix this, is try to make her offer something in return, i.e. to make the drink conditional. Singing is one of my favorite suggestions, but telling a good joke, or even giving you something in return like a cigarette or her seat, should suffice.* Make sure you ask her what she can offer before you suggest something. None of this sounds very foolproof though, so don't try if you are afraid of rejection.
*I try to make girls do these things without offering them drinks, I like to be entertained when I go out
Too bad you walked off, I would have enjoyed to hear what she could come up with. Pretty cool move though
One of the most useful things you will ever learn about body language