Bayer was born in Barcelona on February 13, 1946. Before becoming a mathematician, she was certified as a piano teacher by the
Municipal Conservatory of Barcelona in 1967. She graduated from the University of Barcelona in 1968, and completed her Ph.D. there in 1975. Her dissertation,
Extensiones maximales de un cuerpo global en las que un divisor primo descompone completamente, was jointly supervised by Rafael Mallol Balmaña and
Jürgen Neukirch. She was one of the first two women to earn a Ph.D. from the university; the other was her high school teacher. She was an assistant at
Universität Regensburg from 1977 to 1980. After briefly working for the
University of Santander and
Autonomous University of Barcelona, she joined the faculty at the University of Barcelona in 1982. She retired in 2016. ==Contributions==