He was a lieutenant during the Revolutionary War, serving with the 4th Albany County (NY) Militia. He is also said to have been with Ethan Allen's Green Mountain Boys.
The US Census of 1790 shows Bethuel Barnum, over sixteen, with one free white female, living in Fredericks, Dutchess County, New York. The 1800 census for Delaware County, New York, shows Bethuel Barnum 45 or over, with three males under ten, two females under ten, and one female 26-45.
Both the Genealogical Record of the Barnum Family and The Barnum Family, 1350-1907 suggest the possibility of an additional Bethuel Barnum between Lieutenant Bethuel Barnum and his father Bethuel Barnum (1705-1787), but I have not found reliable evidence to support that contention. In fact, the available evidence seems to support the inclusion of just the two Bethuels, as I've done in this genealogy.
According to the DAR Patriot Index, Bethuel, Jr. is listed as a Private from New York, as was his father. Bethuel was listed in 1810 as Bethuel Barnham, still in Delaware County, town of Rosebury (undoubtedly Roxbury). In 1820 he was still at Roxbury, again listed as Bethuel Barnum. The 1830 listing for Cayuga County is probably Bethuel Baxter Barnum.