Like his brother Thomas he studied at the Jesuit College of St Omer in the Spanish Netherlands.
With the exception of a trip to Piacenza (Italy) in November 1637 Bacon remained in Rome for the rest of his life.
In 1649 he was appointed first pro-secretary and then secretary of the society, a position he held under four successive Superior Generals — Piccolomini, Gottifredi, Nickel, and Oliva.
On retiring from the office in 1668 he served as personal admonitor to Superior General Giovanni Paolo Oliva.
He produced an encyclopedic bibliography in folio, Bibliotheca Scriptorum Societatis Jesu (Rome, 1676), much admired for its thoroughness and latinity, although the listings follow the traditional categorization according to authors' Christian names.