Rose was born on 9 January 1877, the second daughter of Charlotte Sophia Wilson (1853–1924) and Arthur Sidgwick (1840–1920).
In 1902, she enrolled in the Diploma of Education and passed the examination – with Distinction – one year later.
At Somerville College she worked as temporary tutor in history and after a few years, as librarian.
Sidgwick continued her career at the University of Birmingham, where she was appointed as assistant lecturer in History.
During the same visit, she also discussed the founding of a world organisation for higher educated women, with among others Virginia Gildersleeve, Dean of Barnard College, resulting in the launch of International Federation of University Women.