Bastrop is the county seat of Bastrop County, Texas, and is located about thirty miles southeast of Austin, Texas. By 2005, the city had an estimated population of 7,297, up more than 35% from the 2000 census figure of 5,340; its population has doubled since the early 1970s. Bastrop apartments for rent comparison page shows most up to date rent information on Bastrop apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.