I know how this goes, and unfortunately I fail miserably at this, so my advice is probably worth a failure, but:
I have tried twice, and unfortunately, failed twice. The first girl, in retrospect, was a bad person to ask to begin with: she liked another guy, and a guy she can't get. The second girl (I asked her last week) gave me the superbright smile, and had the same reaction as yours, and the next day when she had time to think on it, she said she had to deny me this. I though before hand she liked me, but, learning from the first one, decided not to go emo 😛.
Unfortunately, it looks as if she's putting it off, to delay telling you the bad news. But, if I'm wrong as usual, have fun paying hellish amounts of money on her!