Apartments For Rent In Burnet County Tx . 10 homes for rent in burnet county, tx. To view all affordable housing nationwide, please visit affordablehousing.com. Flats Austin, TX Apartment Finder from www.apartmentfinder.com 159630 for rent, 8.96 acres of land with a 3 bedroom, 2 bath double wide mobile home. Burnet county, tx homes & apartments for rent. Search 3 rental properties in burnet county.