Through her mother, Kira Maria was a granddaughter of Ivan Asen II of Bulgaria and Irene Komnene of Epirus.
She married the Bulgaro-Cuman nobleman George Terter in a marriage arranged by her brother in order to strengthen his position.
He was accordingly made a despotēs, the highest rank in the Byzantino-Bulgarian court hierarchy, and Kira Maria was granted the title of despoina.
Ivan Asen III failed to assert himself throughout the country and he secretly fled Tarnovo in 1280 and escaped to the Byzantine Empire.
Patriarch Yoakim III of Bulgaria threatened to excommunicate the couple and insisted that he would not relent until George I Terter put away Kira Maria.