I believe in being direct.  The realtionship only ended a month ago, and she might still be healing from that.  Call her . . . . ask her to spend the day with you . . . . . go somewhere you can just walk and talk .. . . . . . . . and tell her how you feel.  Tell her that you understand that she just got out of another relationship and that you will go slowly or wait until she is ready.  Be honest.  We don't like BS.  Just be sincere but don't go overboard.  You might overwhelm her and chase her off.  Just tell her that you have always admired her and would love the opportunity to make her happy.