Winston, the reigning Heisman Trophy winner, faces a university disciplinary hearing for an alleged sexual assault in December 2012. Florida State is also investigating whether he was paid to sign autographs by the same company linked to Georgia running back Todd Gurley. Winston was also suspended for the team's game against Clemson this season for yelling an obscene phrase in the college's student union.
Bowden, who coached at Florida State for 34 seasons until 2009 and is the all-time leader in wins, said Winston needs to mature.
"Jameis has got to grow up. He does things that kids in grammar school would do, or kids in junior high would do, you know it? I think once he draws the line, and says 'I'm not going to step below this another time,' I think he can do that. But if he don't, he's going to make it mighty tough on himself."
There was a report earlier this week that Winston's NFL draft stock had taken a hit because of his behavior off the field, but Bowden said he is impressed his performance hasn't been impacted by the controversy.
"I think his draft status has already dropped way down, you know," Bowden said. "But what's amazing to me about him, I don't care what goes on off the field, once he gets under the center, he blocks everything else out. It don't affect the way he plays."
The sophomore has completed 70 percent of his passes for 1,605 yards, 11 touchdowns and five interceptions in five games. As a redshirt freshman last season he threw for 4,057 yards, 40 touchdowns and 10 interceptions en route to leading the Seminoles to the national championship.
Florida State is the No. 2 ranked team in the country and hosts No. 5 Notre Dame on Saturday night.
- Paul Palladino