Bridges began writing and performing 1950s and '60s-style soul music that was described by Austin 360 as "a transmission straight from the heart." He began to attract followers, and his break into the music industry has been attributed to meeting guitarist Austin Jenkins and Joshua Block of White Denim. It was Bridges' performance of "Coming Home" that caught the attention of the two. Bridges worked on his first few tracks with Jenkins and Block as producers. They recorded an album with vintage equipment, using local musicians affiliated with White Denim. Bridges released two demo songs on Soundcloud in late 2014. "Coming Home" received airplay from local radio stations including KKXT. It attracted the attention from a number of record labels with Bridges eventually signing with Columbia Records in December 2014.
Bridges began his first national tour in January 2015, playing shows in Texas as well as playing support for Sharon Van Etten in New York City. His first official single, "Coming Home", was released on Columbia Records in February 2015. The song continued the success of the demo version and became a Top 10 Most Viral Track on Spotify the same month as its release. Bridges toured with Jenkins and Block until they resumed work with White Denim. He also played at the Sundance Film Festival and played at the SXSW festival in 2015.
His debut album was released in the summer of 2015 and has been referred to as a 2015 "Album to Look Forward to From Texans" by The New York Times. Bridges made the cover of Fort Worth, Texas magazine in May 2015 for his vocal accomplishments and his distinctive retro style. "Coming Home" is featured in an Apple iPhone 6 commercial. Bridges made his first appearance in the UK as an artist in May when he sold out the London Village Underground. He went on to announce four July dates, ending with a gig at Shepherd's Bush Empire on September 28. Coming Home was nominated for Best R&B Album at the 58th Annual Grammy Awards.
Aside from his own shows, Bridges also supported Pharrell Williams at the Apple Music Festival on September 26. While opening at the intimate Roundhouse, he was able to perform hits such as "River", "Better Man" and "Lisa Sawyer" from his debut album Coming Home. Bridges was the featured musical guest on Saturday Night Live on December 5, 2015. He performed "Smooth Sailin'" with a full backup band, and sang "River" with only backup singers and organ, accompanying himself on guitar.
Bridges also participated in Macklemore & Ryan Lewis's song "Kevin", which was released on the duo's second full-length album.
On April 8, 2016, Bridges was the live artist featured on BBC Radio London Robert Elms show. Elms interviewed Bridges briefly, and played track 8, "Pull Away", from the Coming Home album. Bridges was set up to play live with Colin O'Brien. Together they performed a live version of "River". The live track was so well received it was played again as "live track of the week" on the Elms Saturday show on April 9, and again on April 11 during a program segment on the best-ever live performances on the Robert Elms show.
The song "River" received further recognition from the 2017 series Big Little Lies and was also included on the soundtrack for the show.
The song "Better Man" was also featured in the 2018 film Pacific Rim Uprising.
On May 18, 2018, Bridges performed "Beyond" from the album Good Thing on an episode of the BBC series The Graham Norton Show.
In 2018, Bridges will be the opening act on the South American and Mexican legs of Harry Styles' first solo tour. Bridges' second album Good Thing was released on May 4, 2018.