Bonacossa was the daughter of Squarcina Borri (1230–1277, also called Scarsini), captain of exiles from Milan from the advent of the Torriani family, and a loyal supporter of the Visconti, and Antonia (1236–?), of unknown lineage, who married in 1254. Borri's family was originally from the town of Santo Stefano Ticino together with some feudal lands of nearby Corby. The Borri family was one of the most respected of Milan, and counted among its ranks a saint, Monas of Milan, Bishop of Milan.
Once the Visconti had conquered Milan, Squarcina Borri gave his daughter in marriage to Matteo I Visconti, Lord of Milan in 1269 to cement those bonds essential to maintaining the rule of the Visconti.
Bonacossa and her husband co-founded of the chapel of St. Thomas in the Basilica of Sant'Eustorgio of Milan, where they were buried, along with their son Stefano and his two daughters Beatrice and Catherine, and the brother of Matteo, Uberto III Visconti.
