Spice things up. Smile. If staring battle continues, add things like ":P" faces, grimaces, etc. After some times, go up to her and say, something like "okay, you win, you're too strong at staring battles. This is the first time I lose one, may I ask your name?".

Would be a fun opener. Don't let this last too long, by the way.

Also while staring battle is happening, don't look away, embarassed, or creepy. Put on a face like you're having fun and/or enjoying this. Ie, smile and suddenly act like you're trying very hard to keep a straight cold face, then crack a smile again.