He was the eleventh and youngest son of Sir Richard Bulkeley of Beaumaris and Cheadle, but the eldest by his second wife, Agnes, daughter of Thomas Needham of Stenton.
When the news reached the city there was a large scale riot, and a mob stoned Bulkeley, who had to seek refuge in a private house; to his outrage, Dublin Corporation refused to take any steps to assist him and refused entry to the town to the troops sent by the Crown to quell the riot.
Bulkeley was one of the Council who in 1646 issued a proclamation confirming the peace treaty concluded in that month between the Marquis of Ormonde and the Roman Catholics.
belonging to the archbishopric of Dublin should be vested in General Henry Ireton, president of Munster, and Bulkeley was committed to prison for resisting the act passed by the English Parliament in 1647, prohibiting the use of the Book of Common Prayer.
The archbishop died at Tallaght on 8 September 1650, in his eighty-second year, and was buried in St. Patrick's Cathedral, Dublin under the communion table.