It is known that he trained as a musician under Antonio Brunelli, most likely in the city of Prato in the 1610s but possibly earlier in San Miniato.
When Brunelli was appointed maestro di cappella of the Grand Duke of Tuscany to the Order of Saint Stephen at the Santo Stefano dei Cavalieri Church in Pisa in 1613 he followed his teacher to that city.
In 1618 Bettini was appointed organist at the Santo Stefano dei Cavalieri, most likely by Brunelli.
The Brunelli volume contains two art songs for solo voice and one vocal trio by Bettini.
The Prague National Museum has additional music by Bettini not published in those volumes, including five secular duets and trios, a single solo aria, and a lettera amorosa.