Dear Ms. LeMay,
Thank you for posting your request on History Hub!
With a birth year of 1753 it seems that the William Bradford you refer to is a New England-based soldier in the American Revolutionary War. According to the Historical Register of Officers of the Continental Army During the War of the Revolution, April 1775, to December, 1783 there were two William Bradfords in New England, and still others elsewhere. There was an Ensign from New Hampshire and a Major in Rhode Island. Further information may be needed to determine which Bradford you are inquiring about.
We searched the National Archives Catalog and located the Compiled Service Records of Soldiers Who Served in the American Army During the Revolutionary War in the War Department Collection of Revolutionary War Records (Record Group 93) that includes a service record of William Bradford. These records have been digitized and are available using the Catalog. It states that Bradford served in Bedel’s Regiment, which was based in New Hampshire and was captured and later exchanged during the invasion of Canada.
Since Major Bradford may have been from Rhode Island, this Genealogical wiki provides information that may be pertinent to Ensign Bradford from New Hampshire given the information you provided. It states that “Major” William Bradford was born in Amherst, New Hampshire in 1753. He married Hannah (Parker) Bradford some time before 1780 in New Hampshire. The findagrave.com page for a Major Bradford and associated pages of his family state that Hannah died in 1812, also in New Hampshire. Bradford then married Lois (Wilkins) Bradford in 1813 in Francestown, New Hampshire. Findagrave also states he had at least two children, Ambrose, who died in 1865, and Lucy (Bradford) Curtis, born 1789 and died 1838. Bradford himself moved to Barre, Vermont and died there in 1816.
While these resources give his rank as Major, the details suggest they are in fact about Ensign Bradford from New Hampshire and that he attained the rank of Major later in life. Furthermore, the Historical Register of Officers linked above states that the Major from Rhode Island died in 1811.
Bradford and family may have spent much of their lives in Hillsborough County, New Hampshire, and Washington County, Vermont. We suggest you make contact with libraries or historical societies in those areas as they might have information about residences and the like.
We hope this is helpful. Best of luck with your family research!