In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
It is preferable for anyone not fasting to refrain from eating in public during Ramadan. This is to protect their own reputation.
Women, in particular, are exempted from fasting during menses. Even if it would be understood by most Muslims that she has an excuse to eat in public, it probably would be a little embarrassing for people to know she is having her menstrual period.
It was the practice of the Prophet (peace be upon him) to cut off the means to suspicion. So, even though you are allowed to eat in public when you are exempted from fasting in Ramadan, it is better to avoid it whenever there might be some room for reasonable suspicion.
Almighty Allah knows best.