Bradshaw was born in Lyman, Wyoming to Melvin K. Bradshaw and his wife the former Lorene Hamblin. He went to junior high school in Salt Lake City and high school in Portland, Oregon while his father oversaw the construction of air landing facilities in the Aleutian islands.
The family then moved back to Lyman, where Bradshaw graduated from high school. Besides Halliday, other Brigham Young University professors of music Bradshaw studied with were Leon Dallin and Crawford Gates. Among those he studied with at Illinois were Carl Fuerstner, Hubert Kessler, and Claire Richards.
Bradshaw did his undergraduate studies at Brigham Young University, where he was mentored by John R. Halliday. After returning from his mission he was accepted into Brigham Young University"s á capella choir. Bradshaw received a masters in music and a doctor of musical arts degree both from the University of Illinois.
In addition to being a professor at Brigham Young University, Bradshaw was also the first to hold the position of composer-in-residence there, also served as executive director of the Barlow Endowment for Music Composition, and directed Brigham Young University"s semester abroad program in Austria on multiple occasions as well.
He worked closely with Ralph Laycock, Brigham Young University"s orchestra conductor, and Ralph Woodward, the conductor of Brigham Young University"s premier choir, in getting his various compositions performed. In addition to his work with Brigham Young University Bradshaw was a key figure in Latter-day Saint music
He was made the head of the composition devision of the Latter- Day Saints (Mormons) Music Department in December 1972. Merrill and Janet Bradshaw had seven children.
