At the age of fourteen or fifteen, she fell in love with Pietro Bonaventuri, a young Florentine clerk in the firm of Salviati, and on 28 November 1563 escaped with him to Florence, where they were married. In 1564 she had a daughter named Virginia, or, according to other sources, Pellegrina. The Venetian government made every effort to have Bianca arrested and brought back but the Grand Duke Cosimo I intervened in her favour and she was left unmolested.
However, she did not get on well with her husband's family, who were very poor and made her do menial work, until at last her beauty attracted Grand Prince Francesco, son and heir apparent of the grand duke.
Although already married to Joanna of Austria, Francesco seduced Bianca and gave her jewels, money and other presents. Bonaventuri, Bianca's husband, was given court employment and consoled himself with other ladies until, in 1572, he was murdered in the streets of Florence in consequence of some amorous intrigue. It is possible that Bianca and Francesco were involved.