His grandfather, Jabez A. Bostwick, was a founder and treasurer of the Standard Oil Company of New York and a partner of John D. Rockefeller.
His father was a horseman and polo player and Pete Bostwick become one of a leading steeplechase owners, trainers, and riders.
In flat racing he finished 4th in the 1928 running of the Belmont Stakes aboard Whisk Broom, owned by his uncle F. Ambrose Clark.
flat race on J. F. Byers' Glaneur then won the Chamblet Memorial steeplechase on Mrs. Ambrose Clark's Madrigal II the same day.
Bostwick also owned Haig Point Plantation on Daufuskie Island off of Hilton Head in South Carolina which he bought from Stiles Harper of Estill, SC in 1961 for $143,000.
Pete married Dolly Van Stade on April 26, 1949 to at the home of her parents in Old Westbury, Long Island.
He won three National squash titles, two hard racquets Open Championships, and was a World Champion in court tennis.