Born in Derby, England to a farm family, William Bancroft was educated in local schools and then earned a drafting scholarship to the Royal Academy in London. He also studied briefly at the University of Manchester.

He ran away from home, and traveled to the American West where he joined General Crook's scouts in Santa Fe, and with his troops fought Apaches for two years in Arizona. In 1878, Bancroft studied for several months at the Saint Louis Art School and then went to Leadville, Colorado where he decorated bars and painted signs. There he met Thomas Moran and accompanied him on a sketching trip.

In 1881, he went to Colorado Springs and painted landscapes and some "trompe l'oeil" still lifes in the manner of William Harnett including a painting titled "The Miner's Last Dollar". He had hard luck financially, and a New York merchant made purchases that provided financial stability.

He created paintings of mining camps and mountain landscapes and did commissioned work for the Santa Fe Railroad that included scenes of the Grand Canyon. Under the tutelage of Harvey Otis Young, Bancroft learned to paint brightly colored landscapes quickly, often finishing them on location in one day.

Sources:
Peggy and Harold Samuels, An Illustrated Encyclopedia of Artists of the American West
Peter Hastings Falk, Editor, Who Was Who in American Art
William Gerdts, Art Across America, Volume III