Your issue is really very easy. Simply go across the hallway to her apartment.ring the bell and when she answers ,introduce yourself. Say something like "my name is (?) and I live in apartment number (?) and I wanted to introduce myself and get to know you. After all we are neighbors who live across from each other." Her response will clue you in on who she is ,get you guys in to the talking mode,maybe into the would you like a drink mode and from there to where ever it leads regardless of your motives and desires.