Do not underestimate the omniscience of school secretaries. Get in good with one of them at the school and carefully ask about yer luv’s relationship situation. The secretaries know; they always know. (Of course, they’ll also know why you’re asking, but if they like you, they won’t let word spread too far too quickly.)
Or, as Nava said, just ask her when an appropriate time has come along.
Find out where she lives. Follow her home. Moon around outside her windows. When she goes out, skulk in the bushes. Then break in and steal some of her underwear from her clothes hamper. After a week, mail it back to her with a passionate letter describing your undying love.
Then drop by her office at the end of the day and ask her to dinner.
Seriously, what ever happened to the simple, tried-and-true, ancient technique of asking a girl to dinner?