Bumpas B. Brinkley was born in Henderson County, Tennessee, probably in Lexington. In 1850 Henderson County, Tennessee shows him with his parents and brothers John and William, living in district 18. Bumpas was 9 at this time. He is found in the 1860 Conway County, Arkansas census, indicating the family had moved at some time before this.

Bumpas married Martha Ann Hill on August 28, 1859 in Union Township, Conway County, Arkansas. There were six known children born to them. He was a farmer and cow dealer.

Due to his service in the Civil War, we have a description of him which reads: Complexion: Light, Eyes: Blue, Hair: Light.

He served in the Arkansas Calvary from December of 1863 to August of 1965, at which time the war ended. Before 1897 he and Martha had moved to Oklahoma.

After Martha's death in Oklahoma, he married Elizabeth Allen on April 3, 1898 in Choctaw Nation. Elizabeth was originally from Alabama. Their one known child, Laura Ethel, died as a baby and is buried at San Bois Cemetery. Bumpas died in Latimer County in Oklahoma at Wilburton.

His name is seen spelled in various ways, including Bumpus and Bumpass.