Of relatively humble origin, Bennett rose with his uncle, also Robert Bennett, successively dean of Windsor (1596) and bishop of Hereford (1603). In 1603 he was granted a five-year lease of a house in Windsor as a servant of the dean.
Bennett served as clerk of the works at Windsor Castle till the Civil War. He played no apparent part in the conflict, but was assessed by Parliament at £1,000 in 1644, and discharged on payment of £140.
