Bryce was born in the town of Dunblane in the then unitary council area of Perth and Kinross, which is today located in the Stirling council area of Scotland. He became a ship's carpenter, converted his faith to the Church of Jesus Christ of Latter-day Saints, and left Scotland for Utah at the age of seventeen.Ebenezer was the only member of his family to convert to Mormonism, and was "disowned" by his father.
Bryce married Mary Park in Salt Lake City in 1854. They moved to southern Utah by 1862, and settled in Pine Valley where Bryce was responsible for designing and overseeing the building of the Pine Valley Chapel in 1868, the oldest Mormon chapel still in continuous use. The chapel is unique in that it was built like an upside down ship using a technique that Bryce acquired as a shipbuilder in Scotland. The chapel is well maintained and is listed on the U.S. National Register of Historic Places.
In 1880, Bryce moved his large family to an area of Arizona, about two miles north of Pima, where the settlement of Bryce is named in his honor. It was there that he died and is buried in a local cemetery.