Practicing Compassion

Have you ever met someone whether its at work, at the store, or through a friend and you watch them loose their sh%t? I recently witnessed a woman answer the phone at receptionist desk make a mistake, and then hang up the phone and walk up and down the hallway flailing her arms "I can't do it" over and over. I know my mouth was hanging open because it was dry and I could not think of ONE thing to say. True to form I turned and walked away, I also talked about her later behind her back. Now I am afraid of her and ashamed of myself.
Id like to say that I am the person that responds every time with compassion, however I am not. If this woman and I had a history or compassion I would have asked her what is wrong, or what can I do to help etc. I would not have turned my back. Perhaps shame begets shame?
The big question is how to do work through our own shame to respond to people in the moment that can prevent them from freaking out? How do you?