On 19 January 1771, he married Elizabeth Tully, daughter of Dr. James Tully, a Dublin physician, and his wife Bridget Netterville, a distant cousin of Viscount Netterville,[3] and had by her four sons.[4] Bradstreet died at his home in Booterstown in County Dublin.[9] He was succeeded in the baronetcy by his oldest son Simon.[4] His widow died in 1799.