Born in Norfolk, Virginia, Scott was a well-known drummer in the local music scene of a region known as Hampton Roads during the early 1980s. Playing with bands in clubs throughout Norfolk, Virginia Beach, Hampton, and Newport News. Travis moved to California in the early/mid 1980s and played in various local bands, such as Hawk, and later on moved to play for the critically acclaimed Racer X, together with Paul Gilbert, and very briefly played in Saints Or Sinners, which later changed their name to The Scream, and also featured Travis's Racer X bandmates Bruce Bouillet and John Alderete. His big career move came about late in the decade after Judas Priest's longtime drummer, Dave Holland, exited the band, citing personal reasons.
Travis had always wanted to be the drummer of Judas Priest. As a young teen, he had often thought about setting up his drumkit in the parking lot at the Hampton Coliseum in hopes that the band would notice him as they went past with their tour bus. He finally decided to wait at the back of the arena to hand the band a tape of his playing. Holland was still the band's drummer at the time, so nothing ever came out of the encounter. When Holland did leave Judas Priest in 1989, Jeff Martin heard about it through his friendship with Rob Halford. Martin called up Travis one day and said "Guess who needs a drummer?" Travis auditioned for the vacant position and in 1989 got the job, thus becoming the first non-Briton to play for the band. Travis has been with the band ever since and he also handles drum duties for his earlier band Racer X. He played drums in Halford's band Fight from 1993 to 1995, but to date is best known for his work with Judas Priest, for which he has been widely acclaimed ever since his debut with Painkiller in 1990.
Travis was also largely responsible for hiring Tim 'Ripper' Owens, as Halford's replacement in Judas Priest in 1996. Owens would remain in Judas Priest until the 2003 reunion. 
He is commonly mistaken to be left-handed. In reality, he is ambidextrous, and plays with an open style.
Scott always used Tama Drums until 2008. On the first leg of the Judas Priest "Nostradamus Tour" he played a Pearl kit and then switched to a DW kit for the second leg. He was also seen using a DW kit at the NAMM show with his band Racer X. His DW setup is: two 23"x24" bass drums, 14"x6.5" snare,8"x8" 10"x9" 12"x9" and 14"x10" rack toms and 16"x14" and 18"x16" floor toms. Scott has played Paiste cymbals since May 1987.