Q: Where did the title Mary Queen of Apostles come from?
A: Mary Queen of Apostles, understood as title/advocation first appears in the oldest version of the Litany of Loreto, those of Paris (end of the twelfth C.) and Padua (end of the fourteenth C.) (see Meersseman II, 222-229). The liturgical feast was approved in 1890 (May 17) requested by the Pallottine Fathers and adopted by a number of dioceses and religious (esp. missionary ) congregations. In the older version of the Missale Romanum it was scheduled for Saturday after Ascension (probably in the neighborhood of May 21 ... now and then!) There were--at one time--seven women's congregations with that name. Many congregations with special apostolic orientation venerate Mary under this title (Salvatorians, Claretians, Pallottines, Missionaries of Steyl, etc.).
The biblical roots of this title (also true for the iconographical theme) are, of course, Acts 1:13-14 showing Mary in the midst of the apostles. The thematic stressing Mary's pre-eminent role with regard to the apostles is much older than the title. In a homily (erroneously attributed to Cyril of Alexandria, PG 77, 992) Mary is pictured as the one who leads every creature to the truth. Why? Because Mary brought forth the light of the world. Through her the apostles announce salvation to the world.