Bainbridge was born at Ashby-de-la-Zouch, in Leicestershire to Robert and Anne (née Everard) Bainbridge. He attended the Free Grammar School in Ashby-de-la-Zouch and then became a student at Emmanuel College, Cambridge. He returned to Ashby where he practiced as a physician for some years, kept a school and studied astronomy. Having removed to London, he was admitted (6 November 1618) a licentiate of the college of physicians, and was noticed due to a publication concerning the comet of 1618. Sir Henry Savile (1549–1622) then appointed him in 1610 to the Savilian chair of astronomy just founded by him at Oxford; Bainbridge was incorporated of Merton College and became, in 1631 and 1635 respectively, junior and senior reader of Linacre's lectures.
He died at Oxford on 3 November 1643. He was a friend of Christopher Heydon, the writer on astrology; and also of John Greaves, his successor to both the Savilian chair and Linacre's lectures.
He wrote An Astronomical Description of the late Comet (1619); Canicularia (1648); and translated Proclus' De Sphaera, and Ptolemy's De Planetarum Hypothesibus (1620). Several manuscript works by him exist in the Library of Trinity College, Dublin.