The Bohr magneton is based on the Bohr model of the atom,
whose principles survived the development of quantum mechanics,
even though it turns out that electrons do not have circular orbits.
It worked fine to explain the hydrogen atom,
but a more complex model was needed to explain heavier elements.
An electron does not orbit the nucleus like a planet orbits the sun
but behaves like a wave.
See also in The book of science:
Readings on wikipedia: