When was that? Certainly wasn't recently. That means every team you played, except your two in-state cupcakes, were bowl teams. That means even Vandy, Missouri, TN and Kentucky.
I highly doubt Clemson has ever played 10 bowl teams in one season, but has probably been close in recent years as the ACC has sent a lot of teams to bowls. They had 12 teams in the 2016-17 bowl season and went 9-3. If you go beyond the regular season that year, Clemson probably got close due to the extra playoff games.
***edit: You peaked my curiosity so I looked it up. Clemson played 10 bowl teams in the 2016 regular season and 13 bowl teams if you count the ACC Championship, the CFP semifinal against Ohio State and the National Championship against Alabama. The only team Clemaon lost to that year was Pittsburgh, who was a bowl team.