Bowles said Brady's absence was discussed in advance and that he will return after next week's preseason game against the Tennessee Titans on Aug. 20.
"This is something we talked about before training camp started," Bowles said. "We allotted this time because he wanted to get in and get chemistry with the guys and go through two weeks of training camp, knowing he wasn't going to play the first two games. He didn't want to take away reps from Blaine [Gabbert] and Kyle [Trask], as well as 'Griff' [Ryan Griffin] going into these next two games, knowing it's something he needs to handle."
When asked if the issue was health-related, Bowles said, "It's a personal issue. That's all I can tell you."
Bowles said he has a "pretty high level of confidence" that Brady will be the starting quarterback in Week 1 at the Dallas Cowboys.
Bowles had previously announced that Brady would not play in the preseason opener Saturday against the Miami Dolphins.
Brady had excused absences Aug. 3 -- his previously scheduled off day and also his 45th birthday -- and last Friday. The Buccaneers as a team were off last Thursday.
Bowles said he did not have concern about missed time, largely because of Brady's experience and work ethic. He said he doesn't believe it will disrupt the offense's progression, even as Brady has worked to gain chemistry with new teammates such as wide receivers Julio Jones and Russell Gage and tight end Kyle Rudolph.
When asked if he was worried Brady's personal issue impacted his commitment to the team, Bowles said, "Per our conversation, I am not worried, no."