Bedell was born in Hudson, New York in 1817, the son of Review Gregory Townsend Bedell of Staten Island and his wife, Penelope Thurston Bedell. In 1822, they moved again, to Philadelphia where his father became the rector of Saint Andrew"s Episcopal Church.
Bedell attended Bristol College, graduating in 1836, and the Virginia Theological Seminary, graduating in 1840.
While an infant, Bedell"s family moved to Fayetteville, North Carolina. Bedell was ordained deacon that same year by his great-uncle, Bishop Richard Channing Moore, and was ordained priest by the same bishop in 1841. After his ordination to the priesthood, he served as rector of Church of the Holy Trinity in West Chester, Pennsylvania.
Two years later, Bedell moved to Church of the Ascension in New York City, where he remained until his elevation to the episcopate.
While there, Bedell earned a doctorate of divinity from Norwich University. In 1845, Bedell married Julia Strong.
They had three children, all of whom died in infancy. Bedell was consecrated assistant in 1859.
He was the 67th bishop in the ECUSA, and was consecrated in Saint Paul"s Church, Richmond, Virginia by Bishops William Meade, Charles Pettit McIlvaine, and John Johns, along with other co-consecrators.
He served as assistant bishop for fourteen years and, during the American Civil War, preached loyalty to the Union. When Bishop McIlvaine died in 1873, Bedell succeeded him as the third In 1875, the diocese was divided into northern and southern parts, and Bedell remained bishop of the northern part, which retained the name "Ohio". Bedell resigned his duties in 1889, owing to physical infirmity, and died in 1892.
