Born in Culpeper County, Virginia in 1776, he moved to Kentucky with an older brother when he was very young. He attended Transylvania Seminary and Transylvania University in Lexington, Kentucky and studied law. He was admitted to the bar about 1800 and commenced practice.

In 1808, Bledsoe was appointed Secretary of State. He was a member of the Kentucky House of Representatives in 1812. Afterwards he was elected as a Democratic Republican to the United States Senate and served from March 4, 1813 until his resignation on December 24, 1814. He then became a member of the Kentucky State Senate in 1817, serving until 1820.

Bledsoe was judge of the Lexington circuit in 1822. He settled in Lexington and was professor of law in Transylvania University. He then became minister in the Disciples Church. He moved to Mississippi in 1833 and to Texas in 1835. He died near Nacogdoches, Texas. He was the uncle of Robert Emmett Bledsoe Baylor, an associate justice of the Texas Supreme Court.