This doesn't change the fact that she has to talk out loud. I don't like to take personal calls at work, either. I usually go out into the hall or somewhere more private. I don't think this is rare behavior.
Push the power button to turn on the screen. Hold the phone to your ear. Wait for the be-beep sound, played quietly through the ears-only speaker. Speak. Keep the phone against your ear. Siri will respond through the ears-only speaker.