The Australian had the benefit of playing on greens softened by overnight rain in Texas, and capitalised to the maximum, providing a quality exhibition of putting which saw him require only 25 putts on Thursday, three of which were 24 feet or longer.
Texan Jimmy Walker is two shots back on six-under, with James Hahn and Ryan Palmer a further two shots off the pace. Master champion Jordan Spieth could only manage a 69 at his home event.
Bowditch got off to a fast start, birding five of his first nine holes to take the turn in 30, before three more birdies on the back nine saw him enter the clubhouse on eight-under.
While Bowditch was out of the blocks quickly, Walker made his move late on, birding four of his last five holes, with accuracy coming into the green his biggest strength on the day.
Hahn will be disappointed not to have finished closer to Bowditch after dropping two shots late on. The American is joined by compatriot Palmer on four-under, while Keegan Bradley, Tom Gillis and John Merrick are a further shot back.
Spieth struggled to get going on Thursday, with a birdie at the par-four first something of a false dawn, as he failed to pick up another shot until the 10th. A bogey at the 14th after finding the rough off the tee saw him drop back to one-under and seven shots off the pace.