Bonnet was born in 1688, as he was christened at Christ Church parish on 29 July 1688. His parents, Edward and Sarah Bonnet, owned an estate of over southeast of Bridgetown, which was bequeathed to Bonnet upon his father's death in 1694. It is not known where Bonnet received his education, but many who knew him described him as bookish, and Judge Nicholas Trott alluded to Bonnet's liberal education when sentencing him. Bonnet married Mary Allamby in Bridgetown on 21 November 1709. They had three sons—Allamby, Edward, and Stede—and a daughter, Mary. Edward's granddaughter, Anne Thomasine Clarke, was the wife of General Robert Haynes, for 36 years Speaker of the Assembly of Barbados.