Bob started playing the alto saxophone at age 13, studied with Phil Woods at a summer music camp and took private lessons with Ira Sullivan.

Weekly gigs at the Sweet Basil in Greenwich Village included Tom Harrell, Jimmy Garrison, Kenny Barron, Albert Dailey, Ben Riley, Mike Nock, and Ron McLure.

Three years later he recorded his fifth album as leader, The Nightbathers, with pianist Paul Bley and guitarist John Abercrombie, which was an experiment in free improvisation.

Mover released another album as leader called You Go to My Head with Rufus Reid, Benny Green, Victor Lewis and Steve Hall.

He released an album recorded in Montreal in 1997 called Television (DSM) featuring John Hicks and Jake Wilkinson.