The 36-year-old American birdied six of the first nine holes on his way to firing a seven-under 64 at Wilmington Country Club in Delaware.
Bradley's front nine score of 29 equalled the lowest of his PGA Tour career, and was good enough for a one-stroke lead over Australian Adam Scott, who grabbed solo second spot with an opening 65.
Irishman Shane Lowry shared third place with Justin Thomas and Harold Varner III a further shot back.
"This is a good start. I'm proud of the way I played," Bradley said. "I made a nice putt on the first hole and just kept it going. It was really a fun day.
"If you hit the ball in the fairway, there are a lot of opportunities. I did that a lot today and the ones I missed I was able to manage."
A large group of seven players follow on four-under 67, including Collin Morikawa, Xander Schauffele, Christiaan Bezuidenhout and Tyrrell Hatton.
The BMW Championship is the second of three FedEx Cup playoff tournaments, with the top 30 on points advancing to next week's season-ending Tour Championship in Atlanta.
Bradley was playing alongside Adam Scott, the 2013 Masters champion, who birdied three of the first six holes before making another trio of birdies late in his round as he settled into second place.
"There was a lot of good solid stuff. I'm very pleased," Scott said.
"I watched Keegan and I was really just trying to follow his lead. He kind of had everything going the way he wanted... I was drafting off him."
Rory McIlroy shared 13th place after an opening 68, though his round would have been far better had it not been for a triple-bogey at the par-3 15th after finding water off the tee and missing a sitter of a putt for double-bogey.
"Just that one tee shot on 15," McIlroy said. "I felt like I had probably half a club too much so I was trying to hit like a cut in there over the water and I just double-crossed it -- and then compounded that by the three-putt.
"But overall the rest of it was pretty good."
FedEx Cup points leader Will Zalatoris could only manage a tie for 34th place after an opening 70.