After getting acquainted with the girl and handing over her key you will have to start following her by stepping through an opened hatch. Keep following Elizabeth until you get to the elevator you've used before to get up here.
Songbird will attack you here and once the attack is over approach the elevator's frame and drop down to a staircase. Continue following Elizabeth until you both get to the top of the monument. Some dramatic scenes will take place here and once they're over you'll find yourself in Booker's office again. The solution is the same as during your previous visit in this place so you must simply open the only door.