A native of Connecticut, Bronson practiced law in Utica, New York, becoming surrogate judge of Oneida County and later, in 1829, attorney general of New York State. From 1836 until 1844 he served as a judge of the New York Supreme Court, and was appointed chief justice in 1845. He was named judge of the court of appeals of New York City in 1847, and collector of the Port of New York in 1853. In 1855 he ran unsuccessfully for governor.