The Barnum Family, 1517-1904 calls him Bushrod Cotton Barnum.
In the 1850 US Census for Potsdam, Saint Lawrence County, New York the family of Bushrod Barnum was enumerated togehter with that of his father, as follows:
Dwelling #211; Family #233
Bushrood [sic] Barnum, 23, M, Farmer, Real property $700, b. Vermont
Lucretia Barnum, 24, F, b. Canada West
Jane McShelory, 18, F, b. Ireland
It appears that Bushrod was in Canada in 1871, since the following entry appears in the 1871 Ontario Census: Barnum, Bushted, Age [44] Birthplace [US] Religion [WM] Ethnic Origin [ENGLISH] Occupation [MERCHANT] District [67] Sub District [I] Division Page [2] Page [98] County [LEE] Description [Bastard Twp.]
From The Ogdensburg Advance, Ogdensburg, NY, Thursday, February 20, 1896: Bushrod C. Barnum, 69 years of age, died at St. Louis on the 4th. He was born and brought up here, but went west about 20 years ago.