Bradley was a native of Worcester, where for some time he conducted a school in which mathematics formed a prominent study.
He settled in London, and on 22 December 1791 was admitted licentiate of the College of Physicians.
His doctoral dissertation was published as De Epispasticorum Usu in variis morbis tractandis.
He published a revised and enlarged edition of Joseph Fox the younger's Medical Dictionary, 1803, and also a Treatise on Worms and other Animals which infest the Human Body, 1813.
On the Prospectus for Rees's Cyclopædia he was credited with writing articles on medicine.