Unionville is an unincorporated community and census-designated place in Bedford County, Tennessee. Its population was 1,394 as of the 2020 census. Unionville has a post office with ZIP code 37180. Unionville was platted in 1827, and named for the fact two rival settlements merged with the new name. A post office has been in operation at Unionville sinc…Unionville is an unincorporated community and census-designated place in Bedford County, Tennessee. Its population was 1,394 as of the 2020 census. Unionville has a post office with ZIP code 37180. Unionville was platted in 1827, and named for the fact two rival settlements merged with the new name. A post office has been in operation at Unionville since 1837.