Speaking with Erin Andrews after their dance, Bolton dedicated the dance to his uncle, who is confined to a wheelchair after suffering an injury in a horse accident last year.
"I know if he could, he'd be slow dancing with his wife, Vicki, right now," an emotional Bolton said, as his grandma and other family members cheered for him from the audience.
Speaking with ET's Cameron Mathison after the show, Bolton and Burgess opened up about the emotional dedication.
"My uncle suffered from a bad horse wreck last year and unfortunately, his walk-away wasn't the same as mine and he wound up in a wheelchair," Bolton shared. "I was just visualizing him being able to dance with my aunt and slow dance, so that kind of connected me a little bit."
"That's pretty good inspiration right there," Burgess added.
Bolton also suffered a life-threatening injury last year when he was bucked off a bull and landed on his neck, breaking the C-2 vertebra in his spine and leaving him temporarily paralyzed. He underwent a spinal fusion operation and has a metal brace implanted around his vertebra, making his participation on the show all the more impressive.
Burgess also opened up about how this week's routine, which earned them a respectable score of 29 out of 40, differed from the red hot country number they pulled off on last week's season premiere.
"This song itself says something so very different to our week one dance and Viennese waltz requires something a little softer," Burgess said of the pair's performance, which was set to "Unlove You" by Jennifer Nettles. "We worked on it a lot. We worked on the intention and how to move as one with each other."
The dance also proved to be less stressful for Bolton, when it comes to his still-healing spinal injury.
"This week was a lot better. Thankfully the waltz was easier on my neck," he explained. "I enjoyed it a lot more."
Burgess, who suffered a serious knee injury last season
that sidelined her for several weeks, revealed that Chmerkovskiy is going to Ohio on Tuesday to receive treatment from the same doctor that helped her heal.
"[The doctor] is absolutely incredible. Got me back in two weeks," Burgess said. "Hopefully, he'll do the same for Maks. We haven't talked about the injury just yet, but he's going to see the doc. I know he'll be all right, but it's so sad to see him not out there tonight."