Bushkin grew up in New York and got his start in Bunny Berigan's band at age 19; he also recorded with Billie Holiday in a small group with Berigan. After playing with Condon, he joined the Tommy Dorsey orchestra in 1940. While playing with Dorsey, he co-wrote the song "Oh, Look at Me Now," which became a hit for Frank Sinatra, the band's vocalist.
After World War II, Bushkin played with the NBC Orchestra and briefly with Goodman, and appeared in Garson Kanin's play The Rat Race as a bandleader. In the 1950s, he performed regularly at the Embers, a jazz club in midtown Manhattan, and led his own groups, recording for Columbia and Capitol. He came out of retirement in the mid 1970s to tour with Bing Crosby, and later played occasionally in New York.