"I'm not [dating anyone]," the professional bull rider-turned-model, 29, told Entertainment Tonight, adding that he is "100 percent" single and "full on" available.
After rumors sparked of a potential romance behind the scenes for the Season 24 Dancing with the Stars pair, Burgess, 31, also insisted, "I am not [dating anyone either]. I am absolutely single."
Bonner and Sharna were given a hard time about their obvious chemistry when they first took the stage together on last week's Dancing with the Stars premiere. In a package that played prior to their dance, Sharna was shown blushing as she met the handsome cowboy on his ranch.
"We have a great chemistry getting to know each other," Sharna said, "but obviously we're three weeks into this thing of having met each other on his ranch and we're having a lot of fun."
While the professional ballroom dancer and Bonner maintain they are just friends, they were spotted enjoying a flirty night out at Cowboy Palace Saloon in Chatsworth, CA, on Tuesday, March 21, the day after the show's debut.
In photos obtained by E! News, Bonner had his arm wrapped around Sharna's neck as she held his hand left hanging in the air above her chest. In addition to practicing their moves, Bonner was also reportedly whispering into his partner's ear and giving her some helpful pointers when playing a friendly game of pool.
"She's really good to get along with," Bonner told ET. "We actually have a lot in common. I think our personalities are real similar, but that can make it kind of challenging too sometimes. I think I get on her nerves a little bit sometimes."
Sharna has made it known she's focused on winning the mirrorball trophy, but she couldn't deny there's at least a spark between the couple.
"Our priorities obviously are getting Bonner through this competition as far as he can possibly go," Sharna explained. "So, in the meantime, we're having a lot of fun getting to know each other and we do have great chemistry."
During the first night of Dancing with the Stars performances, Sharna and Bonner received 22 out of 40 possible judges' points for their cha cha routine, which landed them in ninth place on the leaderboard out of 12 competing couples.