Runaway Bay is a city in Wise County, Texas, lying at the Southern end of Lake Bridgeport. The population was 1,546 in 2020. According to the …Runaway Bay is a city in Wise County, Texas, lying at the Southern end of Lake Bridgeport. The population was 1,546 in 2020. According to the United States Census Bureau, the city has a total area of 6.8 square miles, of which, 2.5 square miles of it is land and 4.3 square miles is water.