Born in 1886, the only son of the Reverend W. C. Bourne in Barnet, Bourne was educated at Rydal School and at Downing College, Cambridge where, in 1908, he received a first class Natural Science Tripos. Granted a senior university scholarship, he entered St Mary's Hospital and, between 1910 and 1911, he had qualified as an MRCS, LRCP (as well as obtaining an MB, BCh, Cambridge, and the FRCS England the following year).
While at Queen Charlotte's, in co-operation with Professor J. H. Burn, he published research papers on uterine action in labour and in response to various drugs. He would hold several residential and other appointments at St Mary's, Queen Charlotte's and the Samaritan until the outbreak of the First World War.
In 1912, he married Bessie Hayward, the eldest daughter of G. W. Hayward, with whom he had three daughters. Enlisting in the British Army, he served as a surgical specialist with the 17th General Hospital in Egypt and the 2nd General Hospital in France between 1914 and 1917 and, in the years following the war, he began a successful consulting practice in obstetrics and gynaecology. In 1929, he was elected a foundation member of the Royal College of Obstetricians and Gynaecologists and, founding its museum in 1938, served as curator of its museum which he built up considerably during the following years.
A yachting and deep sea cruising enthusiast, he was a member of several yacht clubs during the 1930s and, in 1933, won the Royal Corinthian Yacht Club's cup for the best cruiser of the year.
On 14 June 1938, Bourne was arrested after performing an operation without fee at St Mary's Hospital to terminate the pregnancy of six weeks of a 14-year-old girl who had been sexually assaulted by five off-duty British soldiers, officers in the Royal Horse Guards, in a London barracks. She asked at St. Thomas' Hospital, but was sent away on the grounds that she might be carrying a future prime minister. Tried at the Central Criminal Court in July 1938, Bourne was acquitted on charges of procuring abortion as his actions were later defended by The Lancet as "an example of disinterested conduct in consonance with the highest traditions of the profession".
His defence had been based on the Infant Life (Preservation) Act 1929 in which, under British law, the only recognised justification for the termination of a pregnancy was if the life of the woman was in danger.. His defence was that the inevitable subsequent emotional and psychological trauma that the girl would experience would be a risk to her life. If the court recognised this to be a legitimate risk then it would fall under the exceptions to abortions of the Infant life (preservation) act, which they did.
Serving as president of the Obstetrical and Gynaecological Section of the Royal Society of Medicine from 1938 to 1939, Bourne later wrote several important books including A Synopsis of Midwifery and Gynaecology, Recent Advances in Obstetrics and Gynecology with Leslie Williams and was the co-editor of British Obstetric and Gynaecological Practice with Sir Eardley Holland. An advocate of state medicine, Bourne expressed his views in Health of the Future (1942), which gained much attention to the issue in the medical field. During the 1960s, Bourne became a founding member of the Society for the Protection of Unborn Children which was organised in opposition to the Abortion Act 1967. In his memoirs,
Those who plead for an extensive relaxation of the law [against abortion] have no idea of the very many cases where a woman who, during the first three months, makes a most impassioned appeal for her pregnancy to be 'finished,' later, when the baby is born, is thankful indeed that it was not killed while still an embryo. During my long years in practice I have had many a letter of the deepest gratitude for refusing to accede to an early appeal.
He would continue serving as consulting gynaecologist at St Mary's Hospital and to the Samaritan Hospital for Women as well as consulting obstetric surgeon to Queen Charlotte's Hospital before his eventual retirement and death on 30 December 1974, aged 88.