He was born in Dublin, the eldest son of Miles Hussey of Abbey Street (died 1771), a teacher of mathematics.
However, he died in November of the following year, reportedly from gaol fever caught while inspecting a prison.
John Darragh in 1782 built an impressive country house, Darraghville, at Kilcoole, County Wicklow, which still exists, though it has been extensively rebuilt.
Dudley was a member of the popular drinking club called the Monks of the Screw (or the Order of St. Patrick), and he was one of the original shareholders in the Bank of Ireland.
He was remembered as a man "whose amiable qualities, whether considered as friend, senator or judge, make his loss truly irreparable".