Nussbaum grew up in Norwalk, Connecticut, and started to play drums at age 12 after studying piano for five years. He also played bass and saxophone as a teenager. He moved to New York City in 1975 to attend The Davis Center for Performing Arts at City College.[1]
During the early 1980s he continued working with John Scofield in a celebrated trio with Steve Swallow. In 1983 he become a member of the Gil Evans Orchestra and also played with Stan Getz. He later joined the Eliane Elias/Randy Brecker Quartet, Gary Burton, and Toots Thielemans. In 1987 he began touring with the Michael Brecker Quintet. In 1988 they recorded the Grammy-winning "Don't Try This At Home". During 1992 Nussbaum was part of the Carla Bley Big Band and that same year John Abercrombie hired him to complete his organ trio.
Nussbaum has kept active in a wide variety of groups, among them a recently formed quartet "B A N N" with Seamus Blake, Jay Anderson and Oz Noy, a co-op quartet "NUTTREE" (the literal translation of his name, German "Nuss" = "Nut" and "Baum" = "Tree") with Abercrombie, Jerry Bergonzi and Gary Versace, the James Moody Quartet, "We Three" with Dave Liebman and Steve Swallow, the Eliane Elias Trio, "Playing in Traffic" with Steve Swallow and Ohad Talmor, while maintaining an active freelance schedule with prominent artists of every generation such as Steve Swallow, Mike Stern, Dekel Bor, Ravi Coltrane and Bill Charlap among others.