[5] In 1784 he became the rector of Dunbin in the county of Louth, which he resigned upon his collation, on 31 January 1791, to the prebend of Loughgall, or Leval-English in the cathedral church of Armagh.
In 1807, he resigned his prebendal stall of Loughgall to become rector of Donoghmore and was appointed in 1812 as the rectory of Loughgilly.
In 1817 he was appointed to the chancellorship of Armagh, to which he was collated on 23 August, thus succeeding his father after twenty-five years.
As his final preferment, Bisset was appointed by the Marquis of Wellesley, Lord-Lieutenant of Ireland, 1821–1828, to the bishopric of Raphoe.
He built several churches in the diocese and expended a considerable sum of money on the improvement of the palace at Raphoe; and when the parliamentary grant was withdrawn from the Association for the Discountenancing of Vice, he supplied the loss.