There are 1 US Post Offices in Bledsoe County serving a total of 10,247 residents equating to 10,247 residents per post office. It's estimated that approximately 16,355 packages are handled across the 1 county post offices annually. Bledsoe County is a county located in the U.S. state of Tennessee. As of the 2010 census, the population was 12,876. Its county seat is Pikeville.