Just one day after golf's rulemakers proposed a ban on long putters being anchored to the body, Bradley proved his lofty status as a player is underpinned by his all-round game as he reached 17 of 18 greens in regulation at Sherwood Country Club.
While compatriot Nick Watney set the pace with a five-birdie 67 in the elite 18-player event hosted by Tiger Woods, Bradley mixed four birdies with a lone bogey to end a damp, overcast day level with Northern Ireland's Graeme McDowell and Jim Furyk.
Five-times champion Woods, who ended a two-year title drought with a one-shot victory here 12 months ago, was a further stroke back on 70 with fellow Americans Bo Van Pelt and Webb Simpson.
"Today was awesome," said Bradley, who became the first player to win a Major using a belly putter at the 2011 PGA Championship.
"I did have a bad break on the last hole, but I played so solidly all day, that's the only green I missed. If I could have made a few more putts, I probably could have been a lot lower."
Bradley marred his round with a bogey at the par-four 18th where his tee shot ended up against a tree root beside a small rock to the right of the fairway.
"It was a bad break, but also if it didn't hit that root, it probably would have rolled all the way back down that hill. It was a good day, and I'll make a better swing on 18 tomorrow."
Bradley said he had gained extra motivation for the round from Wednesday's announcement by golf's ruling bodies that they wanted to outlaw the practice of anchoring by 2016 in order to preserve the "skill and challenge" of putting.
"Yeah, absolutely," he added. "It would be great to go off and really play well here. I've been catching such flak on Twitter and these other places, it would be good to kind of quiet them a little bit.
"I had a guy yesterday telling me to send my application in to Burger King for 2016. I feel like the USGA (United States Golf Association) has really put an X on our back and really shined a light on us, and I don't know if that's exactly fair.
"When we started putting with it (the belly putter), they were legal, and they still are. It's a sticky situation, and I hope people can see through that. It always feels good to play well, but this feels better almost."
Woods, who is seeking his fourth victory this year after triumphing three times on the US PGA Tour, was delighted to move into contention despite not playing at his best.
"I didn't hit the ball very good today and made a few good par putts to keep the round going," he said after mixing three birdies with a bogey.
"I kept myself in the tournament. Could have easily shot myself out of the tournament but I kept myself in it."
Asked if he was surprised only four players had shot under 70, Woods replied: "No, it's still difficult out there. The wind is puffing around and it's all different directions. The greens are soft, and it's hard to get the ball close."
First round scores from the World Challenge:
67 Nick Watney
69 Keegan Bradley, Graeme McDowell (Northern Ireland), Jim Furyk
70 Bo Van Pelt, Tiger Woods, Webb Simpson
71 Jason Day (Australia), Hunter Mahan, Bubba Watson
73 Matt Kuchar, Jason Dufner, Rickie Fowler, Steve Stricker, Ian Poulter (Britain)
74 Dustin Johnson, Zach Johnson
75 Brandt Snedeker