Dundas joined the East India Company Navy and rose to become captain of from 1786 until 1792. Through the influence of his politically well connected uncle, Henry Dundas, 1st Viscount Melville, he was promoted from captain to president of the Marine Board and superintendent of Bombay from 1792 until 1801, during which time "he had £10,000 a year and accumulated £70,000 or £80,000, with which he returned to England".
On returning to Britain Dundas stood as a member of Parliament for English constituency of Gatton and having won the seat after a contested by-election entered Parliament on 24 January 1803. He would remain in parliament for a little over two years, and although he remained a silent member, like other members of his family he voted in favour of measures that brought Addington administration to an end. In April 1805 he vacated his seat, leaving it at Pitt's disposal.
Very shortly after leaving Parliament, Dundas embarked on a voyage to the East Indies to take up the governorship of Prince of Wales Island. His uncle the Viscount Melville had long hoped to establish a naval arsenal. The newly appointed Lieutenant-Governor of Penang, arrived at the newly created Presidency of the British East India Company, between 18 and 24 September 1805, together with his Council and the subordinate officials, including his Deputy Secretary, Stamford Raffles, who would form his new government. The status of Penang at this time, was such that it was on an equal footing with the three great Presidencies in India — Calcutta, Madras, and Bombay. Dundas was Governor of Prince of Wales Isle from 1805 to 1807. He created a red-light district so that he could control disease without having to discourage business. On board HMS Belliqueux, in the Bay of Bengal, he died on 8 April 1807 just two years after he arrived, ill health from unsanitary conditions taking him, and was buried in Penang a few days later.
Family
Dundas was married twice. In 1790 he married Penelope Ford Lindsay of Dublin. She died in 1802. They had no children. On 5 May 1803 he married Margaret, daughter of John Wedderburn of Ballendean . They had two sons:
Robert Adam, who assumed the surnames of Christopher and then Nisbet-Hamilton. He became a Conservative Member of Parliament.
