Bowditch, the Australian also playing close to his home in the Dallas suburbs, made three putts of at least 24 feet while shooting 30 on the front nine. He had a two-stroke lead over another Texan, Jimmy Walker.
A large gallery cheering him all day, Spieth opened with a birdie but missed two short chances late and settled for a 69.
Defending champion Brendon Todd, playing a group ahead of Spieth, had just one birdie and shot 72.
Danny Lee aced the par-3 17th with a 5-iron from 190 yards and finished at 67.