Born as the son of a farmer on Lidingö island, close to Stockholm, Kurt Bergström married Inga Anderson in 1932, and together they had three children, all girls. He graduated from school in 1910 and completed the first part of his medical education in 1915. In 1920 Bergström became a licensed doctor and earned his doctorate in 1936. In 1920 he travelled to Brazil and Argentina for further studies. After joining the military, he worked as a specialised marine doctor until 1923, in the reserve until 1940. After 1923, Bergström worked as a district physician and medical examiner in various district including Kalmar, Jönköping and Gotland. From 1930-39 he was director of the Visby hospital. He then moved to Jönköping as director of the state hospital for epilepsy. He was an honorary member of various social associations including in the field of animal protection. Bergström eventually died of cerebral hemorrhage. He was appointed Knight of the Order of the North Star and the Order of Vasa.
At the 1912 Olympics, Bergström was a crew member, together with his brother Dick, on the Erna Signe which placed second in both races behind the Norwegian Magda XI in the 12 metres class. Accordingly, the crew was awarded the silver medal. Bergström was also awarded the Shooting Badge in gold.