Bass attended Harvard University, graduating in 1744. He taught and preached in Congregationalist churches, then went to England to be ordained by the bishop of London in May 1752. He had been appointed assistant at St. Paul's Episcopal Church, Newburyport, Massachusetts, in 1749 by the new rector, Matthias Plant, whom he followed as rector in 1753, serving until his death in 1803.

Bass considered himself neutral during the American Revolution, but since he omitted from the church Service all reference to the royal family and the British government, he was accused by the Society for the Propagation of the Gospel in Foreign Parts of supporting the colonists and lost his financial support. In May 1789, the first convention of the Diocese of Massachusetts, meeting in Salem, elected Bass bishop of Massachusetts and Rhode Island but his parish rejected the election because lay delegates did not participate. In 1796 in Boston, Bass was unanimously re-elected bishop of Massachusetts, Rhode Island and Maine, with lay participation, and was consecrated in Philadelphia on May 7, 1797. He also oversaw the churches in New Hampshire and is listed by the Diocese of Rhode Island as its second bishop. Edward Bass was the 7th bishop consecrated for the Episcopal Church.

Bass died on September 10, 1803, just before he was to travel to Portland, Maine. James Morss in his diary, wrote of him, "He felt ill on Saturday and felt he could not preach Sunday night and was concerned about my conducting the Service without him as I had not done so before, but he was dead before Sunday."