The movie, Mr Right, follows the life of three homosexual couples, and is coming to the UK after a US release last year.
BMB’s ad takes the form of a letter to Moir, who provoked outrage after comments she made about the death of former Boyzone singer Stephen Gately, who was gay.
A spokeswoman for BMB said: "Mr Right is a film that appeals to both straight people and
homosexuals... we're anxiously awaiting Moir’s response."
The ad will run in this week's Time Out magazine.
BMB partner Trevor Beattie was one of the film’s producers.