Fifth son of Richard Bateson and Lucy Wheeler Gordon, William Henry Bateson was born on 3 June 1812 in Everton. He was educated at Shrewsbury School, and admitted as pensioner to St John's College on 12 October 1829. He graduated in 1836, senior optime in mathematics and third in the first class of the classical tripos (BA 1836, MA 1839, BD 1846, DD 1857). He was elected to fellowship in 1837 and became second master at Leicester collegiate school. He briefly studied for the bar, being admitted to Lincoln's Inn on 12 April 1836, before taking holy orders. He was ordained deacon on 1 December 1839, and priest c. 1840. Between 1840 and 1843 he was attached to the Cambridgeshire parish of Horningsea, and was Vicar of Madingley 1843-7.
Bateson was a tripos examiner at Cambridge and a successful private classics tutor, before becoming St John's College preacher in 1843, followed by steward, and then Senior Bursar 1846-57; a position from which he was able to restore financial security to St John's. In 1841 he was the Rede Lecturer, and for the period 1848-57 he was Public Orator of the university. Bateson was also a key link between two important reformative committees, serving as secretary to both the 1849 revising syndicate established to modify university statutes, and the 1852 royal commission on Cambridge which recommended general university improvements. Following his success as Senior Bursar, Bateson was elected as Master of St John's in 1857. Later that same year, on 11 June, he married Anna Aiken, with whom he had six children. In 1858, he served the office of Vice-Chancellor of the university, and in 1872 he as one of several academics appointed to the second royal commission on Oxford and Cambridge universities, which investigated the extent of their property and income. A strong believer in the improvement of education, he was on the Cambridge improvement board and was on the governing bodies for Shrewsbury and Rugby Schools. He was also the inaugural chairman of the Perse Girls' School, Cambridge, where he was regarded as an enthusiastic promoter of higher education for women.
Generally thought of as leader of the liberal party in academical matters, Bateson used his positions of Bursar and then Master of St John's to introduce reforms in the College, such as leading other Cambridge clergy in a successful campaign to abolish religious tests and liberalising St John's College statutes in 1848 and 1857. In 1880 he succeeded Chief Justice Cockburn on the 1877 statutory commission and was influential in framing new college statutes for St John's, which were effected in 1882, a year after his death. Bateson was responsible for the construction of the new chapel and lodge at St John's in 1865-9, personally financing the wooden-panelled ceilings, and a few weeks before his death he anonymously donated £500 to college funds. He died in the Master's Lodge on 27 March 1881, and was buried on 31 March in Madingley churchyard.