Regency, TexasRegency is an unincorporated community in Mills County, located in the U.S. state of Texas. According to the Handbook of Texas, the community had a population of 25 in 2000.HistoryRegency is home to the Regency Bridge, a suspension bridge traveling over the Colorado River between Mills and San Saba counties. It is listed on the National Register of Historic Places.EducationToday, the community is served by the Mullin Independent School District.