???
An opening, man.
Do you want to talk to her, or are you just put off or weirded out?
An 'in' is generally best when wanting to talk to someone new, be it the opposite sex or not. IE, a common interest or something to start it off, rather than just awkwardly starting.
Example: A girl you like, you want to talk to her, but feel too afraid, but then you notice she wears Death Note shirts or clothing of the same color you like. Bam, right there you have an opening, or an in, that you can use to strike up a conversation.
Same with this girl; if you actually want to talk to her, this is a natural 'in'. Ask her about her staring and go from there. My point was you already have something to talk about. No harm in asking.