At the end of 1975, Bob went out on his own, leading his own groups around NYC and elsewhere. His first working band featured Tom Harrell (trumpet) and the late Jimmy Garrison (bass). Critic, Chuck Berg, wrote in Downbeat “Mover is a poet/philosopher whose music rings with a profundity that speaks to both heart and mind...Mover´s voice is his own, worth listening to...carefully." From 1976 to the end of 1979, he led his own quartets and quintets every Sunday and Monday night playing to packed houses at Sweet Basil in Greenwich Village.
Featured sidemen included pianists Kenny Barron, Mike Nock, and the late Albert Dailey as well as, bassists Buster Williams, Ron McLure and Denis Irwin, trumpeters Harrell and Claudio Roditi, and most often the underrated master, Ben Riley on drums.
In 1976 and 1977, he made is first two recordings under his own name– On The Move (Choice) and Bob Mover (Vanguard) – the latter, having received a 4 ½ star review in Downbeat Magazine. He worked as a sideman with Duke Jordon, Matthew Gee, Albert Dailey, Vinnie Burke and others and often subbed for Russell Procope in a trio with pianist Brooks Kerr and Duke Ellington’s long time drummer, Sonny Greer. During this period, Bob also co-led a group with Lee Kontiz. They played in concerts and clubs in the USA and Canada and recorded an album under Konitz’s name, Affinity – The Lee Konitz Quintet (Chiaroscuro) (that also received a 4 ½ stars in Downbeat).
In 1981, Bob resided in Boston where he taught improvisation workshops at Berklee College of Music in Boston while holding down regular gigs at Michial’s Pub and Pooh’s Pub with his quartet (Joe Cohn or Mick Goodrich on guitar, the late Charlie LaChapelle on bass and the legendary Boston drummer Bobby Ward). He also played in the quintet of pianist Art Matthews with young trumpeter, Wallace Roney as his front line partner.
Rejoining Chet Baker in March, 1981 they toured France, Belgium, the Nederlands, Austria and Germany while making two recordings – Chet Baker Live at Clubs Salt Peanuts Köln Volumes 1, and 2 (Circle) “an added bonus to these discs is the astounding alto playing of Bob Mover”, (Bob Oakley, Jazz Journal, 1990,Chet Baker the Wages of Lyricism).
Back in New York City in 1982, he recorded once again, for Xanadu, Things Unseen, which also received 5 stars in “The All Music Guide To Recorded Jazz”.