There is nothing wrong with a husband and menstruating wife sharing a bed and having physical contact so long as they stay away from conjugal relations while the husband is fasting. So, a wife in her menses is allowed to sleep beside her fasting husband. Her menses do not affect the validity of his fast.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: There is absolutely nothing wrong for a menstruating wife to sleep next to her fasting husband. The only thing we must observe is to stay away from intimate relations while fasting. It should be a matter of common knowledge that we are not allowed to have sexual intercourse with our wives while they are in a state of menstruation.

As opposed to the practice of certain communities who had strict taboos against physical contacts with their wives during menstruation, Islam taught us that there is nothing wrong with physical contact. The Prophet (peace and blessings be upon him) told us that we are allowed to have all normal contacts with our wives in their state of menstruation except, of course, sexual intercourse. In this regard, he never drew a distinction whether we are fasting or not. In other words, physical contacts and sleeping in the same bed are all permissible while fasting so long as we stay away from conjugal relations while fasting.
In conclusion: there is nothing wrong for your wife in sleeping beside you while she is menstruating, even though you may be fasting. Her menses do not affect the validity of your fast in any way.