He was educated first at the Belfast Academy under his father; entered Trinity College, Dublin, on 2 July 1804, where he obtained a scholarship and graduated A.B.
Meantime he attended a session (1808–1809) at Edinburgh, where he studied moral philosophy, church history, &c., under Dugald Stewart, Hugh Meiklejohn, and others.
In 1821 Bruce came forward as a candidate for the vacant classical and Hebrew chair in the Belfast Academical Institution.
Two-thirds of the Arian vote went against Bruce, in consequence of the hostility hitherto shown to the institution by his family; but Sir Robert Bateson, the episcopalian leader, and Edward Reid of Ramelton, moderator of the general synod, made efforts for Bruce, and he was elected on 27 October by a large majority.
The appointment conciliated a section which had stood aloof from the institution on the ground that it had sympathised with unconstitutional principles in 1798, and ultimately the government grant, which had been withdrawn on that account, was renewed (27 February 1829).
Bruce, still keeping his congregation, held the chair with solid repute till the establishment of the Queen's College (opened November 1849) reduced the Academical Institution to the rank of a high school.
On 20 May 1823 he married Jane Elizabeth (died 27 November 1878, aged 79), only child of William Smith of Barbadoes and Catherine Wentworth.