- In 1960-1961 he worked with Bud Shank and accompanied Peggy Lee, then entered into military service in 1961.
- He was considered to be a member of The Wrecking Crew.
- Budimir learned to play piano and guitar in his youth and first played professionally when he was fourteen years old.
- He recorded in his capacity as studio musician with Joni Mitchell, The Carpenters, Brian Wilson, Barbra Streisand, Ravi Shankar, Frank Zappa, Linda Ronstadt, Julie London, Dusty Springfield, Dave Grusin, Quincy Jones, David Axelrod, Lalo Schifrin, Marty Paich, Don Ellis, Gil Melle, Tom Waits, Harry Nilsson, George Harrison, Ringo Starr, Johnny Mathis, Cher, and Doris Day.
- After his discharge from military service in 1963 he toured Japan with Bobby Troup and returned to the Los Angeles area, where he played as a studio musician for the next several decades.
- In Los Angeles in the mid-1950s he played in a quartet with La Monte Young, Billy Higgins, and Don Cherry.
- In the late 1950s he worked in the bands of Ken Hanna, Keith Williams, Harry James, and Chico Hamilton.
- In jazz idioms he worked with Ella Fitzgerald, Milt Jackson, Stan Getz, Jimmy Smith in the 1970s and with Ray Brown and Johnny Mandel.
- As a session player he also played on more than 900 movie soundtracks from the early 1960s until the 2000s.
- He was an American jazz and rock guitarist.
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