J.S.
I wouldn't criticize Bob at all here, to be honest. Betty hit him with her information AS SOON AS he walked in. It sounds as if she expected a response from him immediately that she gave correct information. She then proceeded to give more details on the conversation she had with a client which forced Bob to give more reaction/response.
It sounds as if he was trying to be gentle with her except she kept snowballing the situation with more and more information, digging herself into a deeper hole. She's the one who didn't give the situation the privacy it required. She should have waited until Bob was in his office and settled in or e-mailed Bob with the information.
Instead, Betty sucker-punched Bob as he was walking in the door. I have a feeling that after you were gone, Bob would also have reprimanded her for airing the company's dirty laundry in front of another client as well as putting him in a position of having to address the issue as soon as he walked in the door.