After a course of study in Edinburgh, he was licensed to preach by the Church of Scotland, but made his way to London in 1721, to teach in schools at Edmonton, Hampstead and Camberwell. in 1777, he settled as minister of the Congregational church at Gosport in Hampshire, where he also took charge of an institution for preparing men for the ministry.
It was the age of the new-born missionary enterprise, and Bogue's academy was largely the seed from which the London Missionary Society grew. Bogue himself would have gone to India in 1796 if not for the opposition of the East India Company. He was also involved in founding the British and Foreign Bible Society and the Religious Tract Society, and in conjunction with James Bennet, minister at Romsey, wrote a well-known History of Dissenters (3 vols., 1809). Another of his writings was an Essay on the Divine Authority of the New Testament. He died at Brighton.