Born in Bowling Green, Kentucky, Bush was exposed to country and bluegrass music at an early age through his father Charlie's record collection, and later by the Flatt & Scruggs television show. Buying his first mandolin at the age of 11, his musical interest was further piqued when he attended the inaugural Roanoke, VA Bluegrass Festival in 1965. As a teen Bush took first place three times in the junior division of the National Oldtime Fiddler's Contest in Weiser, ID. He joined guitarist Wayne Stewart, his mentor and music teacher during Sam's teen years, and banjoist Alan Munde (later of Country Gazette) and the three recorded an instrumental album, Poor Richard's Almanac, in 1969. In the spring of 1970, Bush attended the Fiddlers Convention at Union Grove, NC, and was inspired by the rock-flavored progressive bluegrass of the New Deal String Band. Later that year, he moved to Louisville and joined the Bluegrass Alliance. In the fall of 1971, the band dissolved and reformed as the New Grass Revival.
The New Grass Revival went through numerous personnel changes, with Bush remaining as the sole original member. Bassist and vocalist John Cowan joined in 1974, with banjo ace Béla Fleck and acoustic guitarist Pat Flynn being enlisted in 1981. From 1979 through 1981, the group toured with Leon Russell, opening the shows and backing Russell during his headlining set.
Beginning in 1980, Bush and Cowan periodically jammed with the Nashville-based Duckbutter Blues Band, whose other members were blues guitarist Kenny Lee, drummer Jeff Jones, and bassist Byron House. Bush recorded his debut solo album, Late as Usual, four years later. In 1989, Bush and Fleck joined Mark O'Connor, Jerry Douglas, and Edgar Meyer in an all-star bluegrass band, Strength in Numbers, at the Telluride Bluegrass Festival in Colorado. When the New Grass Revival dissolved in 1989, Bush joined Emmylou Harris' Nash Ramblers, touring and recording with Harris for the next five years.
In 1995, Bush worked as a sideman with Lyle Lovett and Bela Fleck's Flecktones. He formed his own band, featuring Cowan and ex-Nash Ramblers Jon Randall and Larry Atamanuick, shortly before recording his second solo album, Glamour & Grits, in 1996. He released his next album, Howlin' at the Moon, in 1998, with many of the same players and special guests, including Harris, Fleck and J. D. Crowe.
In the winter of 1997, Bush and the New Grass Revival reunited for an appearance on Late Night with Conan O'Brien as the backup band for Garth Brooks. On March 28, 1998, Bush's hometown of Bowling Green, KY, honored him with a special "Sam Bush Day" celebration.
Following Howlin' at the Moon in 1998, he released Ice Caps: Peaks of Telluride in 2000, which was a live recording. In 2004, Randall left Bush's band and Brad Davis took over harmony vocals and guitar duties.
In 2006, Bush released Laps in Seven. The release was significant because it marked the return of the banjo to Bush's recordings, played by Scott Vestal. The guitarist, Keith Sewell, performed on the recording, but shortly after took a job with the Dixie Chicks. Bush sought a new guitarist for his recordings and road band and found Stephen Mougin.
In 2007, Bush released his first live concert DVD, titled On The Road. 2007 also marked the first time he had been chosen to host the International Bluegrass Music Association Awards.
Bush contributed to two bluegrass tribute albums to the British Progressive Rock band the Moody Blues – 2004's Moody Bluegrass: A Nashville Tribute to the Moody Blues, and 2011's Moody Bluegrass TWO...Much Love. Bush provided the lead vocal for the Ray Thomas song "Nice To Be Here" on the latter album.