After his time at Hartford, Bradley took a position at the Rockefeller Foundation as Associate Director for the Arts, Humanities, and Social Sciences, from 1966–1971, and was then President of the Edward W. Hazen Foundation in New Haven, Connecticut from 1971-1984. At The Rockefeller Foundation, he was particularly proud of his work assisting emerging playwrights and theatres in the heydey of the Off-Off-Broadway theatre movement in New York City in the late 1960s and early 1970s, assisting such emerging talents as playwrights Julie Bovasso, Maria Irene Fornes, John Guare, Sam Shepard, Ron Whyte, and Lanford Wilson, as well as theatres such as the artistic leadership of producers such as Ellen Stewart (La MaMa Experimental Theatre Company or LaMaMa, E.T.C.), Joseph Papp (New York Shakespeare Festival - The Public Theater), Wyn Handman (The American Place Theatre), Joe Cino (Caffe Cino), and the theatre at St. Mark's Church in-the-Bowery. His theatre involvement continued in the 1980s when he served as Chair of the Board of Circle Repertory Company in New York City. As President of the Hazen Foundation, he was known for taking creative philanthropic risks by providing crucial seed funding for innovative programs and organizations that often later attracted substantial funding from larger foundations. The reach and influence of the Hazen Foundation under his leadership, therefore, was amplified well beyond the value of the grants awarded.