His career as a professional astronomer began in 1870, when he was elected Savilian professor of astronomy at Oxford.
He was elected fellow of Balliol in 1850 and Savilian professor of geometry in 1861, and in 1874 was appointed keeper of the university museum.
In 1657 he became professor of astronomy at Gresham College, and in 1660 was elected Savilian professor of astronomy at Oxford.
Sir Henry Savile (1549-1622) thereupon appointed him in 1619 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.
In 1643 he was appointed to the Savilian professorship of astronomy at Oxford, but he was deprived of his Gresham professorship for having neglected its duties.