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.

[4][5] After the 1908 earthquake, Bagnera's publications included little research but consisted mainly of his lecture notes, which were of superb quality and polished to a high standard of clarity and accuracy.

[6] In 1909, along with Michele de Franchis, Bagnera received the prix Bordin from the French Academy of Sciences for a work on hyperelliptic surfaces.

Bagnera was elected a member of the Accademia Nazionale dei Lincei and was made an honorary professor of the Washington University in St.