Billy Drewes was born in 1952 on Long Island, New York (Discogs' own artist biography instead gives New York City; this profile follows his official site, the more detailed of the two sources, and flags the conflict rather than picking silently). He moved to Boston in 1970 to pursue music seriously, working there with Tony Bennett, the Boston Symphony and Gary Burton while leading his own groups, before relocating to New York City in 1975.

In New York he quickly found steady work, playing with pianist Kenny Werner, guitarist John Scofield and saxophonist Joe Lovano, and touring in the bands of Lionel Hampton, Eddie Palmieri and Woody Herman. Through Lovano he entered drummer Paul Motian's circle: Drewes joined the Paul Motian Band alongside Lovano and guitarist Bill Frisell for a run that produced Psalm (recorded December 1981 at Tonstudio Bauer, released 1982 on ECM), the group's first album as a working quintet and one of the defining records of Motian's post-Bill Evans, post-Keith Jarrett direction. The same years brought session and touring work with keyboardist Lyle Mays, engagements with the Nikolais Dance Company and the Alvin Ailey American Dance Theater, and early exposure to the Brazilian and Indian music that would resurface throughout his later career.

In 1990, the year drummer Mel Lewis died, Drewes joined the reed section of the band Lewis and Thad Jones had built at the Village Vanguard, continuing on into its next incarnation as the Vanguard Jazz Orchestra and keeping the Monday-night residency running for decades. Through the 1990s his sideman book grew accordingly: he is one of six saxophonists in Gary Smulyan's nonet on Saxophone Mosaic (recorded December 1993, Criss Cross), plays sax and flute on John Scofield's Groove Elation (1995, Blue Note), and shared billing with fellow tenors Dick Oatts and Walt Weiskopf on two SteepleChase co-led dates recorded in 1998 and issued years later as Jam Session, Vol. 13 (an "alto trinity" session with Jon Gordon) and Jam Session, Vol. 18 (a three-tenor session). He also recorded alto and soprano saxophone on Brazilian guitarist Toninho Horta's Moonstone, and tenor saxophone on the Bert Seager Jazz Quintet's Live at the Yardbird Suite (1990).

In August 2006, Drewes played tenor saxophone and clarinet in the nineteen-piece reed and string ensemble Anat Cohen and arranger Oded Lev-Ari assembled for Noir, released in 2007 on Anzic Records as Anat Cohen & The Anzic Orchestra; he sat in the reed section alongside fellow saxophonists Ted Nash and Scott Robinson, and was the only one of the three reed players still with the group when it played the Kennedy Center's Mary Lou Williams Women in Jazz Festival in May 2009. Around the same period he began a long-running project of his own with percussionist Tino Derado's Boston classmate, percussionist Jamey Haddad: the two, along with bassist Ben Street and drummer Satoshi Takeishi, made Derado's Aguacero (2001) and Aguacero Two (2007) for the small PERUN label. That partnership culminated in 2017 with Under One Sun, an eight-musician, five-country ensemble led by Haddad and built entirely from nine tunes Drewes composed, released on Oberlin Music.

Drewes has continued to teach as well as perform, holding an adjunct faculty position in Jazz Studies at New York University's Steinhardt School and conducting improvisation and composition clinics internationally, while still playing Monday nights at the Village Vanguard as part of the Vanguard Jazz Orchestra's ongoing residency.

Drewes built his career on doubling rather than specialization: across more than a hundred recordings he moves between tenor, alto and soprano saxophones, clarinet and flute, and the width of his working record reflects it, from the free-floating small-group writing of Paul Motian's quintet to the tightly charted reed section of a big band to the Middle Eastern and Indian instrumentation of Under One Sun. That range made him equally useful in Gary Smulyan's crowded six-saxophone frontline and in the two-tenor and three-tenor blowing dates that were a SteepleChase house specialty in the late 1990s. As a composer, all nine tunes on Under One Sun are his, written for an ensemble of oud-adjacent kanun, tabla, congas and accordion built around Jamey Haddad's percussion, a departure from the mainstream New York session work that otherwise defines his discography.