OnIslam.net

Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.

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.

Dear sister in Islam, may Allah reward you abundantly for your eagerness to draw near to Him. We invoke Almighty Allah to enable us to reap the fruits of the blessed month, accept our acts of worship, and grant us forgiveness and immunity against the punishment of Hellfire.

It is noteworthy to state that the month of Ramadan is a blessed month and an opportunity for every Muslim to draw near to Allah, to increase his or her morality and spirituality, and to gain abundant reward.

A woman who is not fasting due to her monthly period should observe the sanctity of Ramadan by choosing to eat and drink discreetly rather than making a public display of it. 

In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto,Ontario, Canada, states the following:

You are best advised to observe the sanctity of Ramadan by choosing to do so discreetly rather than making a public display of it.

Having said this, however, I must state that there is nothing wrong for you to eat and drink while you are not fasting due to reasons that are acceptable in the Shari`ah. We know from the authentic sources that the Prophet (peace and blessings be upon him) used to eat and drink in public in order to show people that they are allowed to so while journeying or in jihad. Therefore, we also find the practice of the Prophet's Companions never abstaining from food and drink while they were traveling during the month of Ramadan. Therefore, you need not have any inhibition in this matter.

Allah Almighty knows best.

Excerpted, with slight modifications, from: www.islam.ca.