From 1934 to 1936, he was a member of the board of the Labour Party in Bergen. His father held a doctorate in medicine, but Bøe enrolled in economics studies at the University of Oslo in 1936. In 1940, he received his cand.oecon. degree. In the same year, the Norwegian Price Directorate hired him, but, because Norway was invaded by Germany, he fought against the invaders in the Norwegian Campaign and became a member of the Milorg resistance. In 1942, the Nazi authorities arrested him. From July 1942 to December 1943, he was held in Grini concentration camp. From 1943 to war's end, he was held in Sachsenhausen concentration camp. After the 1945 liberation, he was a secretary for Prime Minister Einar Gerhardsen. From 1945, he was also named to the Economic Coordination Council. From 1946, he served on the Money and Finance Council. In August 1946, he was appointed a State Secretary in the Ministry of Finance.