The history of the Bissett family in Ireland can be studied independently from that of the originally identical family in Scotland, because of their unique experience following their arrival in Ulster in the early or mid-13th century. Here, while still remaining involved in Scottish affairs, the Bissetts would establish themselves as the Lords of the Glens of Antrim and quickly become equally, then eventually more involved in the politics of the Irish province, becoming among the most Gaelicised of all the so-called Anglo-Norman families in Ireland. The heads of the leading branch of the family soon adopted the Gaelic lineage style Mac Eoin Bissett, by which they are known in the Irish annals, and which translates as "Son/Descendant of John Byset", after a prominent ancestor born in Scotland. In a number of English and Anglo-Norman sources the same head of the family is referred to as the Baron Bissett, also with variants.

Donnchadh was a Gall-Gaidhil prince and Scottish magnate in what is now south-western Scotland, whose career stretched from the last quarter of the 12th century until his death in 1250. His father, Gille-Brighde of Galloway, and his uncle, Uhtred of Galloway, were the two rival sons of Fergus, Prince or Lord of Galloway. As a result of Gille-Brighde's conflict with Uhtred and the Scottish monarch William the Lion, Donnchadh became a hostage of King Henry II of England. He probably remained in England for almost a decade before returning north on the death of his father. Although denied succession to all the lands of Galloway, he was granted lordship over Carrick in the north.