His father was the rich merchant Paolo Spada (unrelated to the Spada family of ancient nobility) who had directed him early on to a career in the church. Bernardino studied law in Bologna, Perugia and Rome and received a doctorate. He served in the Papal Curia from 1617. In December 1623 he was appointed papal nuncio to the court of France, in preparation for which he was ordained titular archbishop of Damietta. He served as nuncio until 1627, when he became papal legate in Bologna. He was made a cardinal January 19, 1626 by Pope Urban VIII. When the plague epidemic hit Bologna in 1630/1631, he helped organize the health care system there.
From 1631 he served again in Rome, filling several influential positions in the Curia. In 1632 he purchased what is now called the Palazzo Spada in the rione Regola, facing Piazza Capo di Ferro with a garden looking over the Tiber, and commissioned Francesco Borromini to modify it for him in a more Baroque style, to house his growing collections.
He died in Rome in 1661 and was interred in the family grave in the church of San Girolamo della Carità.
Bernadino had supported the church careers of several of his family members. His nephew Giambattista Spada became cardinal in 1654 and his great-nephew Fabrizio Spada became cardinal in 1675 and Cardinal Secretary of State in 1691.