Bassus was of Italian Roman and Pontian Greek ancestry, who came from a distinguished senatorial family.
Bassus was the son of an elder Pomponius Bassus, the senator who served as consul in 211, and wife Annia Aurelia Faustina, who was a great-granddaughter of the Emperor Marcus Aurelius and wife Faustina the Younger.
His sister was Pomponia Ummidia and through his mother, Bassus was a descendant of the Nerva–Antonine dynasty.
Bassus was born and raised in his mother's large estate in Pisidia.
He held his first consulship in 259 under the reign of the Emperors Valerian and Gallienus.