Bannerman was born at 35 Royal Terrace, Edinburgh. She was the eldest daughter and fourth child of seven children of Robert Boog Watson (1823-1910), minister of the Free Church of Scotland and malacologist, and his wife Janet (1831-1912), daughter of Helen Brodie and the papermaker and philanthropist Alexander Cowan. Between the ages of 2 and 12, she lived in Madeira, where her father was minister at the Scottish church. When the family returned, they spent much time with their maternal aunt, Mrs Cowan, at 35 Royal Terrace on Calton Hill.
Because women were not admitted into Scottish universities, she sat external examinations set by the University of St. Andrews, attaining the qualification of Lady Literate in Arts (LLA) in 1887. She then married Dr William Burney Bannerman, a physician and an officer in the Indian Medical Service (IMS). The couple then moved to India in 1889, taking up residence in Madras (modern-day Chennai), capital of the state of Tamil Nadu on the southeastern seacoast, populated mostly by the Tamil ethnic group. During their 30 years in India, they had four children: daughters Janet (b. 1893) and Day (b. 1896), and sons James "Pat" Patrick (b.1900) and Robert (b. 1902).
The illustrations and settings of Bannerman's books are all about Indians and their culture. Little Black Sambo has ghee, tigers, and a bazaar, The Story of Little Black Mingo has jungle, a mugger (a kind of crocodile), a dhobi, and a mongoose, Little Black Quasha has a bazaar and tigers, and The Story of Little Black Quibba has mangoes and elephants.