He was educated in the state"s schools, graduated from Indiana University, studied and practiced law there, started his political career in Washington, Indiana, and, after his service in the other Washington, returned to Indiana. After graduation from Indiana University in 1869, Bynum studied law.
Although he lived for some time in Washington District of Columbia, he was a lifelong Hoosier. There, he lived out the remainder of his days. He was admitted to the bar in 1872, hung out a shingle, and set up practice in Washington, Indiana.
He was the town"s first City Clerk.
He was City Attorney from 1871 until 1875, and Mayor from 1876 until 1879. In 1880, he moved from Daviess County to Indianapolis.
Bynum was elected as a Democrat to the Forty-ninth and to the four succeeding Congresses (March 4, 1885-March 3, 1895). Foreign part of that time he was House Minority Whip.
On May 17, 1890, Bynum was censured by the House of Representatives for the use of unparliamentary language.
He was an unsuccessful candidate for reelection in 1894 to the Fifty-fourth Congress. Remaining in the nation"s capital, Bynum was active in the organization of the National (Gold-Standard) Democratic Party, in 1896. He chaired its national committee through 1898.
He served on the commission until 1906.
He then returned to Indiana and retired from the practice of law. He died in Indianapolis on October 21, 1927 and was interred in Oak Grove Cemetery, in Washington, Indiana.
He was a member of the Indiana House of Representatives from 1881 until 1885, serving as House Speaker in 1885. In 1900, Bynum was appointed by President McKinley to be a member of a commission to codify the United States" criminal laws.