Bob Gilmore was born in Northern Ireland and studied at the University of York, England, at the University of California, San Diego (on a Fulbright scholarship), and at Queen's University Belfast. His Ph.D (Queen's University, 1992) was an analytical and textual study of the early works of the American composer, theorist and instrument builder Harry Partch. He went on to write Harry Partch: a biography (Yale University Press, 1998), which won an ASCAP-Deems Taylor Award for works of excellence on American music, as did his more recent book, an edition of the collected writings of Partch's student Ben Johnston (Ben Johnston: Maximum Clarity and other writings on music, University of Illinois Press, 2006). His second biographical work Claude Vivier: a Composer's Life was published by University of Rochester Press in 2014. Bob wrote regularly about the new music scene in his native country, Ireland, and contributed liner notes to new music CDs on labels such as Mode, Nonesuch, New World Records, NMC, Touch, Coviello Classics, Unsounds, Orange Mountain Music, Sub Rosa, CPO, and many others. His research was supported by grants from the British Academy and the Arts and Humanities Research Council.

He was the founder member and keyboard player of Trio Scordatura, an Amsterdam-based ensemble performing music using alternative tuning systems. He was the editor of Tempo: a Quarterly Review of Modern Music. He taught at Queen's University Belfast, Dartington College of Arts, Brunel University in London, and in September 2013 began a post as Senior Research Fellow at the Orpheus Institute in Ghent, Belgium.

He died in Amsterdam on 2nd January 2015.