Wright attended public schools and Lincoln Academy at Hinsdale.
He was the chairman of the Committee on Mileage in the fifty-fourth and fifty-fifth congresses. He moved to North Adams, Massachusetts in 1861. In that year, he was appointed chief deputy collector of internal revenue for the tenth district of Massachusetts in 1861.
He resigned from that position in 1865 to engage in mercantile pursuits.
Wright was elected selectman and commissioner for Berkshire County 1884-1887 and acted as chairman for one year. He died in North Adams, Berkshire County, August 14, 1897.
Wright is interred in the Hinsdale Cemetery. Ashley Bascom Wright was son of Charles and Martha Putnum McElwain Wright of Hinsdale, Master of Arts. Charles and Martha were abolitionists in the 1850s, with Charles serving as local leader of the Free Soil Party and Martha running an underground railway station for runaway slaves on their way up the Skyline Trail to free Canada.
Charles" parents, Asahel and Francis Wright of nearby Chester Center, Master of Arts, also ran an underground railway station 20 miles south of Hinsdale on the Skyline Trail.
He was a member of the State executive council in 1890 and 1891 before being elected as a Republican to the fifty-third, fifty-fourth and fifty-fifth congresses, serving from March 4, 1893 until his death.