Bergsma composed works for symphony orchestra, opera, chamber ensembles, solo instruments and choral groups, most of which has been recorded and continues to be available. He received numerous honors and awards, including the Guggenheim Fellowship and awards from the National Endowment for the Arts and the Elizabeth Sprague Coolidge Foundation. In 1992, he was elected to the American Academy of Arts and Letters. A list of these honors is shown below.

In the New Grove Dictionary of American Music, Kurt Stone describes Bergsma's music as "resourceful and imaginative, essentially tonal, texturally conventional and predominantly lyrical."

Born in Oakland, California in 1921, he began his piano studies with his mother, a former opera singer, and also studied viola before concentrating on composition. At sixteen, he had his first composition lessons with Howard Hanson. Later Bergsma studied with Hanson at the Eastman School of Music as well as with Bernard Rogers. From 1938 to 1940, he attended Stanford University but went on to complete his B.A. at Eastman, where he also earned his M.A. in 1943. From 1946 to 1963, he served on the faculty at The Juilliard School in a variety of roles, most notably as chair of the composition department. From 1963 to 1971, Bergsma was chair of the School of Music at the University of Washington, where he remained as professor after retiring from administration.

Abraham Skulsky wrote: " William Bergsma's music has many unusual aspects. Although in every way contemporary in style, it does not conform to any of the major trends which underlie the musical development of our time. While Bergsma's thinking is neither traditional nor conservative, it also cannot be classified with any established style of today or the recent past ... Bergsma's music is primarily linear; he is both a lyricist and a contrapuntist. He possesses not only melodic inventiveness but also a highly developed organizational ability. Although often poetic and meditative, his music has great structural strength and unity as well as a clearly defined logic. One very notable aspect of his music is its character of intimacy. Bergsma has a discerning ear for timbre and subtle combinations of sound, and he is greatly concerned with harmonic spacing as well as harmonic weight." Juilliard Review - Spring,1956.

• Student, Stanford U., 1938-40; teaching fellow, Eastman School of. Music, 1942-44; A.B., U. Rochester, 1942, Mus.M., 1943.
• Faculty Juilliard School Music, N.Y.C., 1946-63, chairman Composition dept., also chairman of the department of Literature and Materials of music, assoc. dean, 1961-63.
• Professor, 1963-86; Director School of Music, U. Wash., Seattle, 1963-71; visiting professor Brooklyn Coll., CUNY, 1972-73.
• Recipient Town Hall commission. for Symphony for Chamber Orch., 1942
• Bearns prize for String Quartet No. 1, 1943
• Koussevitzky Foundation commission, 1943-44
• grant AAAL and Nat. Inst. Arts and Letters, 1945
• award Society for Publication of American Music, 1945
• Guggenheim fellow, 1946, 51
• Collegiate Chorale commission,1946
• Commission. from Carl Fischer, Inc., for 25th anniversary of League of Composers, 1947
• Juilliard Foundation. Commission. 1953, 62
• Louisville commission, 1953
• Elizabeth Sprague Coolidge commission, 1956
• Collegiate Chorale of Ill. Wesleyan U. commission, 1956
• 1st annual Edwin Franco Goldman Memorial commission , 1957
• Harvard Music Society commission, 1961
• Portland Jr. Symphony commission, 1960
• Mid-Am. Chorale commission, 1963
• Music Arts Society La Jolla commission, 1965
• Phi Beta commission 1966
• American Choral Directors Assn. Commission, 1967
• Kansas City Youth Symphony commission, 1967
• Univ. Alabama for Cadek Quarter , 1970
• Poncho and Brechemin Family Foundation commission, 1971
• New Dimensions in Music, 1972
• National Chorale and N.Y. State Council on Arts commission, 1974
• Great Falls Symphony and Symphony Choir, Montana Bicentennial Administration, 1975
• Seattle Symphony Orchestra commission, 1977
• Chamber Music Society of Lincoln Center commission, 1980
• National Endowment Arts grantee, 1985
• Washington State Music Educators grantee, 1988
• Member AAAL, Phi Beta Kappa, Phi Mu Alpha