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 under circumstances his contemporaries and kinfolk could only describe as a significant fall from grace.
Sometimes a volatile being, he earned the sobriquet "Hot headed" Jesse Bledsoe. Besides being a prominent jurist, he was a maternal uncle to many notable individuals including, but not limited to, Robert Emmett Bledsoe Baylor, who studied law under him, Walker Keith Baylor, who served in both chambers of the Alabama Legislature and as a judge, Thomas Chilton, who likewise represented Kentucky in Congress, and William Parish Chilton, a provisional congressman of the Confederacy from Alabama.