Swift plays the flame-haired "other woman" in 1960s-style music video for duo's new single "Babe"

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Taylor Swift is the gift that just keeps on giving for Sugarland: Bandmates Jennifer Nettles and Kristian Bush reveal that Swift is the one who conceptualized the newly released music video for their Swift co-written single, “Babe.”

“She actually reached out to us and said, ‘I’ve got a great idea for the video,’ and she wrote the treatment,” Nettles, 43, told PEOPLE exclusively Wednesday at the CMT Awards.

“And we looked at it,” Bush, 48, added, “and said, ‘Oh my gosh, this is awesome.’”

On top of that, Swift, 28, wrote herself a featured role, playing a red-haired femme fatale in the early 1960s-inspired video, which debuted on Saturday night. Shot only a couple of weeks ago on the Los Angeles set of the AMC hit series Mad Men, it also stars Nettles as the wronged wife and actor Brandon Routh, who plays her philandering husband; Bush appears in the video in multiple roles.

Taylor Swift Sugarland Babe
Taylor Swift in “Babe”
Taylor Swift Sugarland Babe
Brandon Routh and Taylor Swift

The betrayal song, co-written with Train’s Pat Monahan, was originally slated to appear on Swift’s 2012 album, Red, but it didn’t make the final cut. She offered it to Sugarland, who are Big Machine label-mates, for their just-released album, Bigger, and then volunteered to sing background vocals.

“She loves this song,” said Nettles. “She loves our recording of it. She’s been such a champion of ours, not only for many, many years, but also where this project is concerned. She’s just super excited that we’re doing it.”

Monahan was equally thrilled with the country duo’s recording. “Some of you already know that @sugarland has a new single out called #babe that sounds awesome,” he wrote on Instagram after the song was released in April. “I was lucky enough to have written it with @taylorswift and I want to thank Taylor for being so kind, sweet and talented and letting me be a part of her huge life.”

Kristian Bush and Jennifer Nettles
| Credit: Mike Coppola/Getty

Though Swift had the original idea for the video, the duo says they got together before the shoot to collaborate on ideas. “She’s such a pro,” Nettles said, “and she’s easy-going.”

RELATED VIDEO: Taylor Swift Is a Redhead in Sneak Peek of Sugarland’s Mad Men-Inspired ‘Babe’ Music Video

The filming itself was “pretty fun,” Bush told PEOPLE. “It’s great being in such a large-budget sort of medium for this and to be totally relaxed with all the other artists.”

Jennifer Nettles and Kristian Bush
| Credit: John Shearer/Getty

Sugarland has just launched their first tour in six years, and Nettles and Bush both say they feel like they haven’t skipped a beat.

The partners say they’ve already experienced audiences singing along with their new material. “So the excitement for the new music is really palpable,” Nettles said.