Following education at Eton and St. Andrews University he did the Grand Tour, then became Member of Parliament for Richmond, 1763–1768, then for Stirlingshire, 1768–1794.

He was elevated to the peerage as Baron Dundas of Aske in August 1794, and was also Lord Lieutenant and Vice Admiral of Orkney and Shetland, Councillor of state to the Prince of Wales (later George IV), President of the Society of Scottish Antiquaries and Colonel of the North York Militia.

He acquired Marske Hall in North Yorkshire in 1762 after the death of Sir William Lowther, 3rd Baronet.

[1] Dundas followed his father in having an interest in Grangemouth and in the Forth and Clyde Canal, under construction from 1768 to 1790, and he would have been aware of the 1789 trials on the canal of Patrick Miller of Dalswinton's double-hulled paddle boat powered with a steam engine fitted by William Symington.

At a meeting of the canal company's directors on 5 June 1800 Dundas "produced a model of a boat by Captain Schank to be worked by a steam engine by Mr Symington",[citation needed] and it was agreed this should be immediately put in hand.