Bridwell was born in Northview in Webster County in southern Missouri and attended public school in nearby Marshfield, Missouri. After a short time in Oklahoma, Bridwell relocated in 1909 to Wichita Falls.

First involved in the barbed wire and real estate business, he first drilled for oil in 1917 and formed the Cashion Oil Company. In 1921, Bridwell leased ranchland near Nocona, Texas, from the large landholder William T. Waggoner. He found this land rich in petroleum and drilled there in 1921. In 1927, his newly established Bridwell Oil Company owned more than seven hundred wells in Texas, Oklahoma, and four other western states.

During the 1940s and 1950s, Bridwell was the largest independent oil operator in Texas. Bridwell was affiliated with most of the interest groups created to support the oil industry, such as the American Petroleum Institute and the Texas Mid-Continent Oil and Gas Association (now the Texas Oil & Gas Association).