Bernstein was born to a Jewish family in New York City, the son of Selma (née Feinstein, 1901-1991), from Ukraine, and Edward Bernstein (1896-1968), from Austria-Hungary. He was not related to the celebrated Composer and Conductor Leonard Bernstein; but the two men were friends, and even shared a certain physical similarity. Within the world of professional music, they were distinguished from each other by the use of the nicknames Bernstein West (Elmer) and Bernstein East (Leonard). They pronounced their last names differently; Elmer pronounced his (BERN-steen), and Leonard's was (BERN-stine).

Having studied composition under Aaron Copland, Roger Sessions, and Stefan Wolpe, Bernstein also performed as a concert Pianist between 1939 and 1950 and wrote numerous classical compositions, including three orchestral suites, two song cycles, various compositions for viola and piano and for solo piano, and a string quartet. As President of the Young Musicians Foundation, Bernstein became acquainted with classical Guitarist Christopher Parkening and wrote a Concerto for Guitar and Orchestra, which Parkening recorded with the London Symphony Orchestra under Bernstein's baton for the Angel label in 1999. In addition, Bernstein was a professor at the University of Southern California's Thornton School of Music and Conductor of the San Fernando Valley Symphony in the early 1970s.

He received 14 Academy Award nominations and was nominated at least once per decade from the 1950s until the 2000s, but his only win was for Thoroughly Modern Millie for Best Original Music Score. Bernstein was recognized by the Hollywood Foreign Press Association with Golden Globes for his scores for To Kill a Mockingbird and Hawaii. In 1963, he won the Emmy for Excellence in Television for his score of the documentary The Making of The President 1960. He is the recipient of Western Heritage Awards for The Magnificent Seven (1960) and The Hallelujah Trail (1965).

Bernstein wrote the theme songs or other music for more than 200 films and TV shows, including The Magnificent Seven, The Great Escape, The Ten Commandments (1956),True Grit, The Man with the Golden Arm, To Kill a Mockingbird, Robot Monster, and the fanfare used in the National Geographic television specials. His theme for The Magnificent Seven is also familiar to television viewers, as it was used in commercials for Marlboro cigarettes. Bernstein also provided the score to many of the short films of Ray and Charles Eames.

During his childhood, Bernstein performed professionally as a Dancer and an actor, in the latter case playing the part of Caliban in The Tempest on Broadway, and he also won several prizes for his painting. He attended Manhattan's progressive Walden School and gravitated toward music at the age of twelve, at which time he was given a scholarship in piano by Henriette Michelson, a Juilliard Teacher who guided him throughout his entire career as a Pianist. She took him to play some of his improvisations for Composer Aaron Copland, who was encouraging and selected Israel Citkowitz as a Teacher for the young boy. Bernstein's music has some stylistic similarities to Copland's music, most notably in his western scores, particularly sections of Big Jake, in the Gregory Peck film Amazing Grace and Chuck, and in his spirited score for the 1958 film adaptation of Erskine Caldwell's novel God's Little Acre.

Throughout his life, Bernstein demonstrated an enthusiasm for an even wider spectrum of the arts than his childhood interests would imply and, in 1959, when he was scoring The Story on Page One, he considered becoming a Novelist and asked the film's Screenwriter, Clifford Odets, to give him lessons in writing fiction.

In 1961 Bernstein co-founded Äva Records an American record label based in Los Angeles together with Fred Astaire, Jackie Mills and Tommy Wolf.

In addition to his film music, Bernstein wrote the scores for two Broadway musicals, How Now, Dow Jones, with lyricist Carolyn Leigh, in 1967 and Merlin, with lyricist Don Black, in 1983.

One of Bernstein's tunes has since gained a lasting place in U.S. college Sports culture. In 1968, University of South Carolina football head coach Paul Dietzel wrote new lyrics to "Step to the Rear", from How Now, Dow Jones. The South Carolina version of the tune, "The Fighting Gamecocks Lead the Way", has been the school's fight song ever since.

When Martin Scorsese announced that he was re-making Cape Fear, Bernstein adapted Bernard Herrmann's original score to the new film. Bernstein leapt at the opportunity to work with Scorsese, as well as to pay homage to Herrmann. Scorsese and Bernstein subsequently worked together on two more films, The Age of Innocence (1993) and Bringing Out the Dead (1999). Bernstein had previously conducted Herrmann's original unused score for Alfred Hitchcock's 1966 Torn Curtain.

In 1996, Bernstein was honored with a star on Hollywood Boulevard. In 1999, he received an Honorary Doctorate of Music from Five Towns College in New York City and was honored by the American Film Institute in Los Angeles. Bernstein again was honored by ASCAP with its marquee Founders Award in 2001 and with the NARAS Governors Award in June 2004.

Bernstein made his home in Hope Ranch in Santa Barbara, California, in the 1990s. Bernstein died of cancer in his sleep at his Ojai, California, home on August 18, 2004. His publicist stated that he had a lengthy illness. He left behind his wife, Eve, two sons Peter and Gregory, and two daughters, Emilie and Elizabeth. He had five grandchildren at the time of his death.