Price graduated from the University of Mississippi with an engineering degree in 1902. He married Maggie L. "Lutie" Bragg on November 23, 1904 in Mississippi County, Mississippi. They had two children, Lutie Price (1911–1995) and Bem Jr (1917–1985).
Price moved to Birmingham and joined prolific architect David O. Whilldin as partner in the firm of Whilldin & Price in 1910. With Whilldin he worked on Walker County High School in Jasper, two schools in Anniston and a residence in Gadsden. The partnership dissolved in 1911 and Price moved his office into the newly-built Comer Building in 1913.
Price was one of the charter members of the Alabama Chapter of the American Institute of Architects, organized in 1916. About that time he was working on plans for the Limestone County Courthouse in Athens. He was also commissioned to design the new Minor High School which opened in 1922. He was involved in the collaborative design of Municipal Auditorium in 1923.
- Limestone County Courthouse, 1918, Athens
- Tupelo High School, Tupelo, Mississippi
- Peabody Building, University of Mississippi, Oxford
- Minor High School, 1922, Adamsville
- Dormitory, Athens College, 1916, Athens, Alabama
- Municipal Auditorium, 1924
- tower and education building, Highlands United Methodist Church, 1924
- William Bankhead residence, 1924, Jasper
- Birmingham Fire Station No. 4, 1926