David Allen Moore graduated Summa Cum Laude from the USC Thornton School of Music in 1993 where he studied with Dennis Trembly, Paul Ellison, and John Clayton. Moore continued his studies in Boston, working privately with BSO principal bass Edwin Barker while performing with Boston Baroque, the Rhode Island Philharmonic, Emmanuel Music, and the Boston Pops Esplanade orchestra. Moore performed as a substitute with the Los Angeles Philharmonic during the 1995-96 season, after which he was a member of the Houston Symphony bass section under maestro Christoph Eschenbach, from 1996 to 1999.

In 2000, Moore joined the bass section of the Los Angeles Philharmonic.

Moore has participated in numerous festivals including Tanglewood, the Grand Teton Music Festival, Mainly Mozart, and Kent/Blossom Summer Music Festival. He is an active recitalist and chamber musician, having performed in the Houston area with the Greenbriar Consortium, in Los Angeles with the Philharmonic's New Music Group, and in San Diego with the Mainly Mozart Festival. He was also a featured clinician at the 1999 Texas Double Bass Symposium. From 2003-2009 Moore was a faculty member at the Colburn Conservatory in Los Angeles. Moore has been a faculty member of the University of Southern California's Thornton School of Music since 2000, and in the fall of 2010 joined the full-time faculty there while maintaining his position in the Los Angeles Philharmonic. Since 2007 Moore has been a faculty member at Domaine Forget in Quebec, Canada.

In 2007, he began studies with internationally renowned double bass pedagogue and soloist François Rabbath in Paris. Moore received both the Diploma and Teaching Certificate from the Institut International Rabbath in February of 2009.

Moore has presented masterclasses in the United States and Canada at The Curtis Institute, Juilliard Conservatory, Rice University, New England Conservatory, Peabody Conservatory, The Glenn Gould School, Northwestern University, and Boston University among others.

The double bass that Moore performs on with the Philharmonic is an instrument by Nicolo Gagliano made in 1735. His solo bass is a modern instrument by French luthier Christian Laborie. Moore uses bows designed especially for him by Parisian bowmaker Boris Fritsch that are a unique French/German hybrid designed to be played either overhand or underhand.