Bryant's even-par 72 gave him a 10-under 134 in the fourth of five majors on the Champions Tour this year.
Bryant built a big lead with a first-round 62 that matched the tournament record. Tom Watson shot 62 in the second round in 2003, when the tournament was played in Aloha, and Doug Tewell had a final-round 62 in 2001, when the event was held in Scottsdale, Arizona.
Bryant's two-birdie, two-bogey second round was just enough to hold the lead entering the weekend. His best finish this year was fourth at the Dick's Sporting Goods Open in June.
He has four overall Tour victories, his last at the Senior U.S. Open in 2007.
Funk was coming off a victory at the U.S. Senior Open, where he became the first player in a USGA championship to finish 20-under-par. A week earlier, he lost in a three-way playoff at the Senior British Open.
Funk has finished in the top-10 in the previous three Champions Tour majors this season and leads the Charles Schwab Cup points standings.
Roberts won the Tradition in 2005 and has won twice on the Tour this year, including the Senior British Open. The eight-time winner on the PGA TOUR recovered after a double-bogey on the par-4 eighth hole to shoot 71 on Friday.
"It's an attitude thing, it's a confidence thing," Roberts said. "If you have confidence in your game, you can get over it."
Watson wasn't so lucky. After two bogeys and a double bogey on the front nine, he fell off the leaderboard and finished with a 74 to put him 3-under entering the weekend.
He nonetheless had one of the biggest galleries on the 7,533-yard course built in the shadow of Mt. Bachelor. Watson has said this week that he's encountered many well-wishers in the past month, after losing in a playoff to Stewart Cink at the British Open.
Watson won the Tradition in 2003.
Cook, who has struggled on the Champions Tour since winning last year's AT&T Championship, shot a 67, as did Mize, who just joined the Tour last year.
"No bogeys for me, and that's always a good thing," Cook said.