Bell was born in Bloomington, Indiana, United States, the son of a psychologist and a therapist. Bell's father is the late Alan P. Bell, Ph.D., Professor Emeritus of Indiana University, in Bloomington, a former Kinsey researcher.

Bell began taking violin lessons at the age of four after his mother discovered her son had taken rubber bands from around the house and stretched them across the handles of his dresser drawer to pluck out music he had heard her play on the piano. His parents got a scaled-to-size violin for their then five-year-old son and started giving him lessons. A bright student, Bell took to the instrument but lived an otherwise normal midwest Indiana life playing video games and excelling at sports, namely tennis and bowling, even placing in a national tennis tournament at the age of ten.

Bell studied as a boy first under Mimi Zweig, then switched to the renowned violinist and pedagogue Josef Gingold after Bell's parents assured Gingold that they were not interested in pushing their son in the study of the violin but simply wanted him to have the best teacher for his abilities. Satisfied that the boy was living a normal life, Gingold took Bell on as his student. By 12 Bell was serious about the instrument, thanks in large part to the Gingold's inspiration.

At the age of fourteen, Bell appeared as a soloist with the Philadelphia Orchestra conducted by Riccardo Muti. He studied the violin at the Indiana University Jacobs School of Music, while managing to graduate from Bloomington High School North in 1984, two years ahead of schedule. In 1989, Bell received an Artist Diploma in Violin Performance from Indiana University. His alma mater also honored him with a Distinguished Alumni Service Award only two years after his graduation. He has been named an “Indiana Living Legend” and received the Indiana Governor’s Arts Award.