At the University of Palermo, Bagnera received his "laurea" in civil engineering in 1890 and then his "laurea" in mathematics in 1895. His teachers included Giovanni Battista Guccia, Francesco Gerbaldi ed Ernesto Cesàro. In 1899 he was appointed "libero docente" (lecturer) in algebraic analysis at the University of Palermo. He was appointed professor extraordinarius of infinitesimal calculus in 1901, then professor ordinarius in 1905, at the University of Messina, where he remained until the 1908 earthquake. He then taught at the University of Palermo until 1922 when he moved to the Sapienza University of Rome, where he taught until his death.