[3][2] Dundas joined the East India Company Navy and rose to become captain of Melville Castle from 1786 until 1792.
[4] 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 (see Admiral-superintendent), during which time "he had £10,000 a year and accumulated £70,000 or £80,000, with which he returned to England".
[6] Very shortly after leaving Parliament, Dundas embarked on a voyage to the East Indies to take up the governorship of Prince of Wales Island.
[citation needed] The status of Penang (comprising Prince of Wales' Island and Province Wellesley) at this time, was such that it was on an equal footing with the three great Presidencies in India — Calcutta, Madras, and Bombay.
[10][citation needed][11] On board HMS Belliqueux, in the Bay of Bengal, he died on 8 April 1807 just two years after he arrived,[12] ill health from unsanitary conditions taking him,[2] and was buried in Penang a few days later.