The High School Musical 2 actor, 24, says he hurt his thumb and that his partner, Karina Smirnoff, also got minor injuries from practicing their routine.
"The first day my thumb kinda popped in and out of its socket and it was swollen," Bleu tells PEOPLE. "And her back is all scraped up from me dragging her on the floor on a move."
Bleu says that Smirnoff "is quite the whip-cracker" and that the pair have a team nickname that reflects how hard they're been working.
"We've decided that our team middle name is gonna be 'One more time,' " he says. "Because every single time we finish [the routine], one of us says, 'No, no, no, one more time!' "
Bleu admits that he needs the extra practice, because even though he's had dance training, ballroom is new to him.
"Karina was really excited when I first came in. She wanted to test me out with a bit of a quick step, and she was kind of assuming, 'oh, he dances, he'll be fine,' " he says. "And we were wrong. She said, 'we have some work to do.' "
Bleu adds that although Smirnoff is putting him through the paces, he is enjoying the process. "She is hardworking and she is working me really hard. I'm having a blast, though."