In 1699 he graduated in philosophy and law at the University of Siena. In 1701, immediately after studying canon law, he began his ecclesiastical career, which led him to take religious orders in 1705 and to hold the position of archdeacon in 1723. He had a brilliant academic career, becoming president of the Academy of Physiocritics. In 1737 he wrote the essay that made him famous: Discorso sopra la Maremma di Siena. Bandini considered this economic text so important that two years later he decided to offer the manuscript version to the Grand Duke of Tuscany, Francis I of Lorraine. The text not only addressed the need to recover the Maremma, but also all the interventions necessary for the economic development of a territory. According to Bandini, it was necessary to have few and extremely simple economic laws so that they were easily understood. According to him, too many rules and regulations actually led to a decline in trade and, consequently, to an impoverishment of the territory. The work was only published in 1775, under the reign of Pietro Leopoldo, who was inspired by Bandini's theories for his economic policy.
His great love for culture led him to accumulate such a large quantity of books and manuscripts that they became a real library, which he donated to the city of Siena in 1758, a year before his death. The donation included almost three thousand volumes, which were brought to the Palazzo della Sapienza and formed the original nucleus of the current Municipal Library of the Intronati. With the donation, Bandini entrusted his precious library to one of his students, the abbot Giuseppe Ciaccheri, also providing him with a salary. The trust was well founded, since Ciaccheri quickly increased the library, which after fifteen years included about thirteen thousand volumes.