The song was not in one of the "Ziegfield Follies," but sung by Lillian Lorraine in the musical "Miss Innocence," starring Anna Held.
I don't believe that the song was included at the opening but added later.

My grandparents had the sheetmusic, the Heath-O'Donnell version, which is the one I remember. Traditional it ain't. (Who is this Springsteen? -he, he, he!).