On the death of Bishop Porcher, the Chapter of Cavaillon elected Bertrand Romey of Cavaillon, but the Pope voided the election and appointed Palamedes de Carreto: Étienne Antoine Granget (1862). Histoire de diocèse d'Avignon et des anciens diocèses dont il est formé (in French). Vol. Tome premier. Avignon: Seguin. p. 601. Eubel, II, p. 123.
He was the author of a treatise, "Il gentilhuomo", Pompeo Rocchi (1568). Il gentilhuomo (in Italian). Lucca: Busdraghi.
Bordini was a friend, and sometimes, secretary of Filippo Neri, the founder of the Oratory: Alfonso Capecelatro (1882). The Life of Saint Philip Neri: Apostle of Rome. Vol. II. London: Burns & Oates. pp. 349–352. He wrote a Life of Pope Sixtus V (1588) and a Life of St. Teresa of Avila (1601).
He had been Chamberlain of Urban VIII, Canon of San Lorenzo in Damaso, Vice-Governor of Tivoli, and Vice-Governor of Ravenna. He was consecrated in Rome in Santa Maria Maggiore by Cardinal Francesco Barberini. He returned to Rome in 1663, where he died on 25 June. Jean Antoine Pithon-Curt (1750). Histoire de la noblesse du Comté-Venaissin, d'Avignon, et de la principauté d'Orange, dressée sur les preuves (in French). Vol. Tome III. Paris: De Lormel & Fils. p. 183.