The Australian sits on 13-under, two shots clear of a group of five players that includes Dustin Johnson, and second round co-leaders Jimmy Walker and Jon Curran. Home town favourite Jordan Spieth is six shots off the pace.
Early thundershowers at the TPC Four Seasons held up the completion of the second rounds that had been carried over into Saturday after rain on the opening two days. However, sunny skies soon found their way to Irving, with the remainder of the day's play going off as planned.
With the par-four 14th still playing as a pitch-and-putt of just over 100 yards due to unplayable fairways, the tournament is thought to be the first in more 30 years to be played to a par-69.
Bowditch started well, registering birdies at the third, sixth and seventh before registering his lone bogey of the day at the ninth after his drive to the right found one of the course's many marsh-like patches and he was forced to take a penalty drop.
Having shared the lead with Bowditch after 36 holes, Curran and Walker could only muster 67s on Saturday to fall two shots off the pace. They're joined at 11-under by Johnson who fired an impressive 62.
Johnson produced a bogey-free round on the traditional mover's day, with the American notching up four birdies in five holes from the second to the fifth to take the turn in 31. A further three birdies on the back nine ensured Johnson 24 places up the leaderboard and very much in contention for his second win of the year after triumphing at the WGC-Cadillac Championship at Doral.
Also at 11-under are Jonathan Randolph and Scott Pinckney who shot rounds of 65 and 64 respectively.
Spieth had to settle for a 68 on a day that promised so much more for the Masters champion. Speaking after the round, the world number two conceded that he just "didn't have it" on Saturday and was "just a little bit off".
The Texas native's round was perhaps summed up on the par-3 17th. Playing in front of a large gallery on the banks to the right, Spieth was inches away from an ace, but saw his ball roll back to eight feet from the hole. With the crowd having gone wild and Speith himself having showed a fair amount of excitement on the tee, the 21-year-old then left his putt on the lip of the cup.