Born in Bologna into a wealthy family with a lawyer as a father, she was privately educated and tutored for seven years in her teens by Gaetano Tacconi. She came to the attention of Cardinal Prospero Lambertini who encouraged her in her scientific work.
She was appointed professor of anatomy in 1731 at the University of Bologna at the age of 21, was elected to the Academy of the Institute for Sciences in 1732 and the next year, in 1733, was given the chair of philosophy. Her teaching opportunities were restricted in her early years, giving only occasional lectures. In 1738 she married Giuseppe Veratti, a fellow academic with whom she had eight children (some sources say more). After this, she was able to lecture from home on a regular basis and successfully petitioned the University for more responsibility and a higher salary to allow her to purchase her own equipment.
She was mainly interested in Newtonian physics and taught courses on the subject for 28 years. She was one of the key figures in introducing Newton's ideas of physics and natural philosophy to Italy. She also carried out experiments of her own in all aspects of physics. In her lifetime she published 28 papers, the vast majority of these on physics and hydraulics, though she did not write any books.
In 1745 Lambertini (now Pope Benedict XIV) established an elite group of 25 scholars known as the Benedettini ('Benedictines', named after himself.) Bassi pressed hard to be appointed to this group, but there was a mixed reaction from the other academics with strong support from some but others taking a negative point of view. Ultimately Benedict did appoint her to the final position, the only woman in the group.
In 1776, at the age of 65, she was appointed to the chair in experimental physics by the Institute of Sciences, with her husband as a teaching assistant. Two years later she died having made physics into a lifelong career and broken a huge amount of ground for women in academic circles.