Henry Bruce was born at Duffryn, Aberdare, Glamorganshire, the son of John Bruce, a Glamorganshire landowner, and his first wife Sarah, daughter of Reverend Hugh Williams Austin. John Bruce's original family name was Knight, but on coming of age in 1805 he assumed the name of Bruce: his mother, through whom he inherited the Duffryn estate, was the daughter of William Bruce, high sheriff of Glamorganshire.
Henry was educated from the age of twelve at the Bishop Gore School, Swansea (Swansea Grammar School). In 1837 he was called to the bar from Lincoln's Inn. Shortly after he had begun to practice, the discovery of coal beneath the Duffryn and other Aberdare Valley estates brought his family great wealth. From 1847 to 1854 Bruce was stipendiary magistrate for Merthyr Tydfil and Aberdare, resigning the position in the latter year, after entering parliament as Liberal member for Merthyr Tydfil.
Bruce was returned unopposed as MP for Merthyr Tydfil in December 1852, following the death of Sir John Guest. He did so with the enthusiastic support of the late member's political allies, notably the iron masters of Dowlais, and he was thereafter regarded by his political opponents, most notably in the Aberdare Valley, as their nominee. Even so, Bruce's parliamentary record demonstrated support for liberal policies, with the exception of the ballot. The electorate in the constituency at this time remained relatively small, excluding the vast majority of the working classes.
Significantly, however, Bruce's relationship with the miners of the Aberdare Valley, in particular, deteriorated as a result of the Aberdare Strike of 1857-8. In a speech to a large audience of miners at the Aberdare Market Hall, Bruce sought to strike a conciliatory tone in persuading the miners to return to work. In a second speech, however, he delivered a broadside against the trade union movement generally, referring to the violence engendered elsewhere as a result of strikes and to alleged examples of intimidation and violence in the immediate locality. The strike damaged his reputation and may well have contributed to his eventual election defeat ten years later. In 1855, Bruce was appointed a trustee of the Dowlais Iron Company and played a role in the further development of the iron industry.
In November 1862, after nearly ten years in Parliament, he became Under-Secretary of State for the Home Department, and held that office until April 1864. He became a Privy Councillor and a Charity Commissioner for England and Wales in 1864, when he was moved to be Vice-President of the Council of Education.