Budimir aprendió a tocar el piano y la guitarra desde muy joven e hizo su debut como profesional con tan sólo catorce años. Durante los años 50 tocó en las bandas lideradas por Ken Hanna, Keith Williams, Harry James y Chico Hamilton.^[2]​ En 1960-1961 trabajó con Bud Shank como acompañante de Peggy Lee. En 1963 realizó una gira por Japón junto a Bobby Troup y cuando regresó a Los Ángeles comenzó una prolífica carrera como músico de sesión que duraría varias décadas.^[3]​ Grabó con artistas como Julie London, Dave Grusin, Quincy Jones, Lalo Schifrin, Marty Paich, Don Ellis, Gil Melle, George Harrison, Ringo Starr, Johnny Mathis y Doris Day.^[4]​ Como guitarrista de jazz participó en grabaciones de Milt Jackson, Ray Brown y Johnny Mandel. 

• The Creeper (Mainstream, 1965)
• Alone Together (Revelation, 1965)
• A Second Coming (Revelation, 1968)
• Sprung Free (Revelation, 1968)
• The Session with Albert (Revelation, 1972)
• The Soul of Dennis Budimir (2012)

Con Rosemary Clooney

• 1996 Dedicated to Nelson
• 1997 Mothers & Daughters

Con Michael Feinstein

• 1987 Remember: Michael Feinstein Sings Irving Berlin
• 1999 Big City Rhythms

Con The 5th Dimension

• 1969 The Age of Aquarius
• 1970 The July 5th Album
• 1970 Portrait
• 1975 Earthbound

Con Chico Hamilton

• 1959 Gongs East!
• 1959 The Three Faces of Chico

Con Quincy Jones

• The Hot Rock OST (Prophesy, 1972)

Con Peggy Lee

• 1961 Basin Street East Proudly Presents Miss Peggy Lee
• 1961 Blues Cross Country
• 1974 Let's Love
• 1975 Mirrors
• 1979 Close Enough for Love

Con Sergio Mendes

• 1973 Love Music
• 1975 Sergio Mendes
• 1976 Homecooking

Con Harry Nilsson

• 1968 Aerial Ballet
• 1971 The Point!
• 1975 Duit on Mon Dei
• 1976 That's the Way It Is

Con Robert Palmer

• 1988 Heavy Nova
• 1990 Don't Explain
• 1992 Ridin' High

Con Van Dyke Parks

• 1968 Song Cycle
• 1989 Tokyo Rose
• 1995 Orange Crate Art con Brian Wilson

Con The Partridge Family

• 1970 The Partridge Family Album
• 1971 Sound Magazine
• 1971 Up to Date
• 1972 A Partridge Family Christmas Card
• 1972 Shopping Bag
• 1973 Crossword Puzzle

Con Linda Ronstadt

• 1983 What's New
• 1986 For Sentimental Reasons

Con Tom Scott

• 1967 The Honeysuckle Breeze
• 1975 Tom Scott in L.A.
• 1976 Blow It Out

Otros artistas

• 1959 Hot & Cool Latin, Eric Dolphy
• 1962 Improvisations, Ravi Shankar^[5]​
• 1965 Wonderful Life, Irene Kral
• 1966 Feelin' Kinda Blues, Gerald Wilson
• 1967 A Spoonful of Jazz, Bud Shank
• 1967 Evergreen, Volume 2, Stone Poneys
• 1968 For You My Love, Lou Rawls
• 1968 Lumpy Gravy, Frank Zappa
• 1968 The Birds, The Bees & The Monkees, The Monkees
• 1970 Black, Brown and Beautiful, Oliver Nelson^[6]​
• 1971 Desiderata, Les Crane
• 1972 Cherish, David Cassidy
• 1972 Free Again, Gene Ammons
• 1973 You've Got It Bad Girl, Quincy Jones
• 1974 Good Old Boys, Randy Newman
• 1974 Payne & Pleasure, Freda Payne
• 1974 Waitress in a Donut Shop, Maria Muldaur
• 1974 Who Is This Bitch Anyway?, Marlena Shaw
• 1975 I Am Music, Carmen McRae
• 1975 Love Me by Name, Lesley Gore
• 1975 Making Music, Bill Withers
• 1975 Mellow Madness, Quincy Jones
• 1975 Montara, Bobby Hutcherson
• 1975 Skull Session, Oliver Nelson
• 1975 Song for My Lady, Jon Lucien
• 1976 Barbara Carroll, Barbara Carroll
• 1976 Can't Hide Love, Carmen McRae
• 1976 Feelings, Milt Jackson
• 1976 I'm Easy, Keith Carradine
• 1976 Warm & Sonny, Sonny Criss
• 1977 Captain Fingers, Lee Ritenour
• 1977 Sweetbird, Lani Hall
• 1978 Don't Cry Out Loud, Melissa Manchester
• 1978 I'm Always Dancin' to the Music, Benny Golson
• 1978 In the Center, Rodney Franklin
• 1978 Songbird, Barbra Streisand
• 1978 Soul Believer, Milt Jackson
• 1979 Hard Times for Lovers, Judy Collins
• 1979 Living Without Your Love, Dusty Springfield
• 1980 Children of the World, Stan Getz
• 1980 Rodney Franklin, Rodney Franklin
• 1981 Big Mouth, Milt Jackson
• 1981 Juice, Juice Newton
• 1981 Made in America, The Carpenters
• 1981 Stop & Smell the Roses, Ringo Starr
• 1982 One from the Heart, Tom Waits/Crystal Gayle
• 1983 Swordfishtrombones, Tom Waits
• 1983 Voice of the Heart, The Carpenters
• 1987 Today, Perry Como
• 1989 Love Julie, Julie Andrews
• 1989 Old Gringo, Lee Holdridge
• 1990 From Brazil with Love, Roberto Carlos
• 1990 My Favorite Things, Monica Lewis
• 1991 16 Most Requested Songs, Teresa Brewer
• 1991 For the Boys, Bette Midler
• 1991 Unforgettable: With Love, Natalie Cole
• 1992 Good Medicine, Doc Severinsen
• 1992 In Tribute, Diane Schuur
• 1992 Swings Jule Styne, Monica Lewis
• 1993 A Touch of Music in the Night, Michael Crawford
• 1993 How Do You Keep the Music Playing, Johnny Mathis
• 1993 Les McCann Anthology: Relationships, Les McCann
• 1994 Love, Nancy, Nancy Wilson
• 1995 If My Heart Had Wings, Melissa Manchester
• 1995 In a Hefti Bag, Frank Capp Juggernaut
• 1995 Now & Then, Dolores Hope
• 1995 Yesterday & Today, Toots Thielemans
• 1996 Blue Condition, Bobby Caldwell
• 1996 In My Lifetime, Neil Diamond
• 1997 Move Over Darling, Doris Day
• 1997 The Wilsons, The Wilsons
• 1998 Bathhouse Betty, Bette Midler
• 1998 Manilow Sings Sinatra, Barry Manilow
• 1998 Mythical Kings and Iguanas/Reflections in a Mud Puddle, Dory Previn
• 1999 1961–1966, Ann-Margret
• 1999 A Christmas to Remember, Amy Grant
• 1999 Complete Capitol Recordings of Gene Krupa and Harry James, Gene Krupa
• 1999 Rosebud, Harriet Schock
• 2000 West Coast Sessions, John Pisano
• 2001 Keely Sings Sinatra, Keely Smith
• 2001 The Best of the Pacific Jazz Years, Richard Holmes
• 2002 It Had to Be You, Rod Stewart
• 2002 The Season for Romance, Lee Ann Womack
• 2003 Lucien Romantico, Jon Lucien
• 2003 The First Sessions, Warren Zevon
• 2003 Trumpet Evolution, Arturo Sandoval
• 2004 Blue Skies, Diana DeGarmo
• 2004 Dreams, Diana DeGarmo
• 2004 Hartman for Lovers, Johnny Hartman
• 2004 Just for a Thrill, Ronnie Milsap
• 2004 Reneé Olstead, Renee Olstead
• 2004 Rick's Rarities 1964-1974, Rick Nelson
• 2005 Sandy Nelson's Big Sixties All-Nighter!, Sandy Nelson
• 2007 Summer in the City, Quincy Jones
• 2012 Stones/Journey to Bliss, Emil Richards
• 2013 Made in California, The Beach Boys
• 2014 Holiday Wishes, Idina Menzel
• 2016 Good Times!, The Monkees^[7]​