Born in Fairmount Indiana and raised on a farm, Olive Rush graduated from the Fiarmount Academy, a Friends Academy established by her parents on their farm. At age seventeen, she went to Richmond, Indiana and enrolled for a year ar Earldom College as a student of John Elwood Bundy, who became a key inspiration to her focus on art and love of painting. She then traveled to Washington, D.C. and studied at the Corcoran School of Art. From 1894 to 1898, Rush was enrolled at the Art Students League in New York. She earned money as a staff artist for the New York Tribune, and in 1898, received her first commission to illustrate a book.
Sailing for Europe in 1910, Rush settled in Paris for a year and studied at the Richard Miller Class for Painters. She later credited his influence for her approach to portraiture and spoke of her time in Paris as stimulating a life-long fascination with Oriental art. She then returned to the states and pursued more art instruction, studying with Frank Benson, William Paxton and Edmund Tarbell at the Boston Museum School in Massachusetts. For the next five years Rush worked as a commercial artist in New York City but soon returned to be closer to her family. In Indianapolis, Rush created portraits that "had a delicate, flowerlike handling and a spiritual quality," and many of her commissions were child portraiture.
After spending several years in Indianapolis, Rush settled in Santa Fe, New Mexico for the remainder of her life. She stated that her experience in New Mexico "opened up a whole new world for me" and led her to focus much more on her own painting. Her move in 1920 meant she was one of the first eastern artist to move to the Southwest. Her residence was on Canyon Road near the home and studio of printmaker Gustave Baumann. She began working with fresco for mural decoration of her own home, and found a recipe with sand and plaster that would last in the New Mexico climate. She was successful in her project and numerous people requested her to do murals for their adobe structures, including public town buildings. In 1929, for the dining room of the La Fonda Hotel, owned by the Santa Fe Railroad, she did fresco decoration that had New Mexican figure scenes, native plants and animals. Because of her success with this project, she was hired by the head of the Santa Fe Indian School to oversee mural painting by the students. Rush also created murals for the Public Works Art Project, and decorated post offices.
Rush is known as one of the early 20th century American women to be fully dedicated as an art professional, and has been described as one of the most competent muralists of that era. Her lasting influence is the encouragement she gave native Americans to take pride in their own traditions at a time when white culture was moving aggressively westward, and her focus was to preserve the arts and crafts of these people.