Dunbar was born in Palmer, Massachusetts, on March 3, 1804. In 1832 he graduated from Williams College, and later, he graduated from the Auburn Theological Seminary. While a student at the latter institution, he received an appointment as a missionary to the western Indians; was ordained at Ithaca, New York on May 1, 1834, and on the 5th left there for the west, with plans of crossing the Rocky Mountains to minister to the Nez Perce. However, upon arriving at St. Louis, Missouri, on May 23rd, he learned that the party of traders with whom he was to travel had already left, and this changed his entire plan.
At St. Louis, he was informed that the Pawnee tribe needed missionaries, and he decided to go there. As soon as possible, he reported at the mission and agency at Bellevue, Nebraska, nine miles above the mouth of the Platte River, on the west bank of the Missouri River, and began his work as a missionary. In September 1836, he returned to Massachusetts, and while there superintended the printing of a 74-page book in the Pawnee language. On January 12, 1837, he married Esther Smith, and the following spring, returned to Bellevue. Later he went to Holt County, Missouri, but preferring a residence in a free state, and confident that Kansas was to be admitted as such, he moved to Brown County, Kansas in 1856, taking up residence on the Wolf River about two miles west of Robinson. On March 16, 1857, he was appointed treasurer to the Board of County Commissioners, being the first man ever to hold that office in the County. Neither Mr. Dunbar nor his wife lived long after they moved to Kansas. She died on November 4, 1856, and his death occurred on November 3, 1857.