Drusus Julius Caesar
It has been theorized that her mother was Julia Livia (daughter of Drusus Julius Caesar and Livilla), which would make Bassa the great-granddaughter of Tiberius and the great-great-niece of Augustus through his sister Octavia the Younger; however, this lineage is uncertain because her father, Gaius Rubellius Blandus married Julia when he was around 55, which makes an earlier marriage likely (possibly to a Laecania Bassa), and Rubellia Bassa may have been the daughter of Blandus by this theorized earlier marriage.