How should I handle my mother's bitchy responses to my attempts at conversation?

Today I was at my parents’ house for Thanksgiving dinner. While my mom was setting the table, I asked her about the neighbor and what she was doing today. The conversation went like this:

Me: Is Mary seeing her son today?
Mom: (cold tone of voice) I don’t know. I don’t monitor her activities.
Me: I’m not saying you monitor her activities. All I’m asking is if she is seeing her son today.
Mom: I have no idea. I don’t question her about what she does.
Me: You don’t have to be so harsh with your words. All you have to say is that you don’t know

When my mother acts bitchy like that it makes me not want to talk to her, and therefore, we will be in the same room with minimal conversation on my part.

Is there a better response I can give her that shuts down her disrespectful tone or should I not even try?