There are at least 3 artists named Bill Bell: An American rockabilly singer, An American jazz pianist and an American fiddle player.
Bill Bell & the 4 Unknowns recorded the 7" single, Little Bitty Girl/Fearless (instrumental), (Mida Records 112), in 1959 in Miami, Florida.

Bill Bell (William Bell Jr., East Moline, Illinois, July 12, 1936 - March 18, 2017) was an American jazz pianist, keyboard player, arranger, composer and music educator. In and around San Francisco he became known as The Jazz Professor.
Bell received music lessons (also in arranging) at home, also from a nephew, a music teacher. He studied music education at the Augustana College (Bachelor, 1958) and at the University of Iowa (Master). He taught in Iowa and moved to the West Coast in the 1960s. In 1966 he first took up with Roy Eldridge (The Nifty Cat Strikes West). In the decades that followed, he gave music classes at the College of Alameda and taught jazz improvisation at the University of California in Berkeley. He also led the jazz band at the Stanford University. His students were Sheila E., Benny Green, Michael Wolfe and Jon Faddis. He also composed, East Meets West (for the Oakland Youth Symphony) and Right On (for the San Francisco Symphony). Under his own name he made the albums Basically / To Live and Love (1979, with Coke Escovedo and Marvin Holmes), The Jazz Professor (1995), Just Swing Baby (2005) and The Feeling of Jazz (2009).
He played with Benny Carter, Clark Terry, Lou Rawls, Louie Bellson, The Supremes, Art Farmer and Carmen McRae. He died in 2017 in Oakland, California.

Fiddle player
Bill Bell's latest CD The Vicar's Son delves into traditional and contemporary Irish, Scottish and American fiddle music...but that's only a small slice of Bell's musical interests. He originally 'discovered' and produced the infamous Del Rubio Triplets, and wrote and co-produced Josey Cotton's album 'Frightened By Nightingales'. His music has led him to Africa, performing with raga outfits and to write and perform his own avant-garde orchestral compositions. The Vicar's Son includes folk tunes Bell has picked up on his travels in the British Isles as well as his own inspired tunes. He imbues the recordings with beauty and care, bringing in top of the line musicians Paul Burton, Eddie Young,Dan Richardson, Enrique Platas and Red Dice to provide sensitive background accompaniment. The result is warm, inviting folk music in an historical context with Bell's contemporary twist...as you can hear in the title track. This is friendly, unaffected music by an equally friendly and unaffected artist, with just enough mystery to provide an edge. Music that is presented with warmth and just a touch of slyness. According to Bill: I found my fiddle in a pawn shop in Lubbock Texas in November 1983. It is labelled 'Aldric' Paris France, 1828. I hope you enjoy listening to 'The Vicar's Son' which is, after all, just a fancy way of saying "Preacher's Kid". Read more on Last.fm. User-contributed text is available under the Creative Commons By-SA License; additional terms may apply.