Bertie was one of the commissioners of assessment for Oxfordshire from 1677 to 1680. When Lord Gerard raised a troop of horse in 1678 in anticipation of a war with France, Bertie was commissioned a captain; the troop was disbanded in the following year. In 1678, after Thomas Wancklyn was expelled from the House of Commons, he was nominated for the vacant Parliamentary seat at Westbury on the interest of his elder brother, Lord Norreys, whose wife was a part owner of the manor of Westbury. The Berties, representing the court party, were opposed by a local squire, William Trenchard, a Presbyterian. Henry was returned by 21 votes to 13; two election petitions by Trenchard and the opposition to overturn the result were defeated. It is not clear that he was active in the Cavalier Parliament, and in December, he was sent for in custody for non-attendance. In the general election of March 1679, he was defeated by Trenchard and Richard Lewis, the other sitting member. Appointed a commissioner of assessment for Buckinghamshire and a justice of the peace for Oxfordshire in 1679, he and Lewis defeated the two exclusionist candidates, Trenchard and Edward Norton at Westbury in the general election of October 1679. He was not appointed to any committees in the subsequent Exclusion Bill Parliament; during 1680, he was taken off both commissions of assessment, although he was made a deputy lieutenant of Oxfordshire, and in November, an election petition by Trenchard and Norton was accepted by Parliament. Bertie and Lewis were turned out and the returning officer, the mayor of Westbury, was confined for two weeks for "great misdemeanours" in making the return.