That left Bowditch two ahead of American Jimmy Walker, a fellow Texas resident who mixed seven birdies with a lone bogey to surge up the leaderboard.
Two more Americans, James Hahn and Ryan Palmer, were a further stroke back after opening with 65s while world number two and local favourite Spieth had to settle for a 69 after making just two birdies and one bogey in the afternoon wave.
Bowditch, whose sole PGA Tour victory came at last year's Texas Open, totalled only 25 putts as he capitalised on a morning tee-off and a fast start.
"It was really nice," the Australian told PGA Tour Radio after piling up eight birdies in a bogey-free display on a course saturated by heavy rain over the past month.
"I got off to a pretty good start, made a couple of putts early and had some momentum."
Bowditch, a top junior player whose professional career was temporarily stalled as he battled depression, set the tone for his day as he recorded birdies at the first, fourth, sixth, seventh and ninth to reach the turn in five-under 30.
"I kept it in the fairway and that's a big thing out here, being so wet," he said. "I stayed aggressive, kept hitting drivers and getting them on the golf course.
"The greens are great. They are soft but you can still make some putts out there."
Spieth made a promising start by sinking a nine-footer for birdie at the par-four first but picked up just one more shot, at the 10th, before bogeying the par-four 14th after his tee shot ended up in the right rough.
"It was tough to putt on today," said Dallas resident Spieth, a double winner on the 2014-15 PGA Tour. "I feel good with the putter in my hands, just maybe not quite matching line and speed.
"The greens were soft and there was so much (afternoon) traffic that putts weren't breaking as much. I think they will be a little quicker tomorrow and more pure.
"Just get out there and try and make a couple of birdies at the beginning, see if we can't get some more (putts) to go in. I only made one mistake today, other than that it was a flawless round."
(Reporting by Frank Pingue/Greg Stutchbury)
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