There are 2 US Post Offices in Trimble County serving a total of 8,535 residents equating to 4,268 residents per post office. It's estimated that approximately 13,623 packages are handled across the 2 county post offices annually. Trimble County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 8,809. Its county seat is Bedford. The county was founded in 1837 and is named for Robert Trimble. Trimble is a prohibition or dry county. Trimble County is part of the Louisville/Jefferson County, KY\u2013IN Metropolitan Statistical Area."