The American had folllowed up his stunning opening round of 60 with a one-under-par 69 in Texas on Friday.
On Saturday he dropped shots at the fifth and sixth holes, but three birdies saw him turn two shots ahead of Tom Gillis.
Gillis began the day three shots adrift in second and he made a perfect start with a birdie at the first.
He then produced a consistent front nine with another birdie at the ninth and no bogeys.
South Korea's Bae Sang-moon had a mixed first nine holes, with birdies at the first two holes and the eighth and a bogey at the fifth.
Harris English was part of an eight-way tie for fourth after three successive birdies saw him turn at eight under overall.
He was joined by the likes of Charl Schwartzel and Martin Kaymer.
Despite seeing his lead trimmed from three shots to one, Bradley was pleased with his day's work and quietly fancied his chances heading into Sunday.
"I played really solid today - one of the most solid rounds of the year - so I'm really excited," the 26-year-old, who won this event two years ago, said on www.pgatour.com.
"I'm going to need to shoot a solid round tomorrow [Sunday]. These guys are playing really good golf. There's a lot of really good players at the top of the leaderboard. But if I go out there and shoot a good round, I like my chances."
And the 2011 USPGA champion has particularly set his sights on mastering the troublesome final hole.
"Tomorrow's the day," he said. "I'm going to hit it right down the middle tomorrow, hit it on the green and make birdie!"