Sir Henry Bunbury, 3rd Baronet (29 November 1676 – 12 February 1733) was a British Tory politician.
He was the son of Sir Henry Bunbury, 2nd Baronet and his wife Mary Eyton, daughter of Sir Kenrick Eyton. In 1687, aged only eleven, he succeeded his father as baronet. Bunbury was educated at St Catharine's College, Cambridge.
Bunbury was High Sheriff of Cheshire in 1699. A year later, he entered the English House of Commons as Member of Parliament (MP) for Chester, representing the constituency also in the British House of Commons until 1727. In 1711, Bunbury was appointed Commissioner of the Revenue for Ireland, a post he held until 1715.
On 15 May 1699, he married Susannah Hanmer, only surviving daughter of William Hanmer (the second son of Sir Thomas Hanmer, 2nd Baronet), and had by her four sons and five daughters. Bunbury died in 1733 and was buried in Stoke, Chester four days later. He was succeeded in the baronetcy successively by his sons Charles and William. His daughter Isabella married General John Lee, and was mother of Continental General Charles Lee.