Later he became Senior Consistory President and Privy Councillor (Wirklicher Geheimrat).He received advancement through the good offices of the Cabinet Minister of the Electors of Saxony, Count von Hoym, the uncle of his second wife.

In 1734, after Hoym had been ousted by Count Brühl, Heinrich von Bünau was downgraded to the position of Senior Overseer of the County of Mansfeld in Eisleben.

In 1741 however he entered the service of the Emperor Charles VII, who made him an Imperial Privy Councillor (Reichshofrat), the first Protestant to fill that role, and employed him as an ambassador in the area of Upper and Lower Saxony.

In 1751 Bünau was appointed as Guardian Governor of the Duchy of Saxe-Eisenach, during the minority of Duke Ernest Augustus II, for whom in 1756 he became Prime Minister in Weimar.

[3] after his death Ossmannstedt was used as a summer house by the Duchess Anna Amalia of Saxe-Weimar-Eisenach (widow of Ernest Augustus II, Duke of Saxe-Weimar-Eisenach and aunt to Queen Caroline of England) and her sons between 1762 and 1775.Heinrich was married three times: 1) In 1721 he married firstly Augusta Helena von Döring (15 November 1706 - 04 November 1728), heiress of Dahlen Castle, great-granddaughter of David von Döring (1577-1638), Privy Councillor of John George I, Elector of Saxony.