Bohun was educated at Queens' College, Cambridge. In the late 1660s he associated with William Sancroft, Samuel Parker and Leoline Jenkins, in a group of High Church proto-Tory thinkers. He began to write against the Whigs after the Exclusion Crisis of the 1680s. He attacked Whig theories and in particular Algernon Sidney in his Defence of Sir Robert Filmer (1684). Sancroft asked Bohun to edit Robert Filmer’s works, for an edition of 1685, and its preface Bohun attacked James Tyrrell.
In reply to Jeremy Collier's The Desertion discuss'd in a Letter to a Country Gentleman (1688), Bohun wrote The History of the Desertion (1690), bringing forward an argument influential for Tories who (unlike Collier) were prepared to swear allegiance after the Glorious Revolution; this work was the first history written of the events in which James II of England left the throne. He drew on the work of Grotius, in De Jure Belli ac Pacis, for the idea of conquest after a just war as applicable to the contemporary United Kingdom, as was also done by William King.
In 1692 he was appointed Licenser of the Press, a position as pre-publication censor. He ran into trouble in the case of an anonymous pamphlet, King William and Queen Mary Conquerors which was really by Charles Blount. It argued a case similar to Bohun's own view. Thomas Babington Macaulay claimed that the Whig Blount in writing it deliberately set out to entrap the unpopular Bohun, but this is no longer accepted. In a House of Commons debate in 1693, Tories defending Bohun pointed out that the bishops Gilbert Burnet and William Lloyd had published similar arguments. The outcome was that Bohun lost the position, which was shortly abolished, and Burnet's Pastoral Letter of 1689 was included in a suppression order covering William and Queen Mary Conquerors. Bohun was briefly imprisoned, and after a two-year renewal of the Press Act providing for a Licenser as censor to 1695, the pre-publication censorship of the press was allowed by Parliament to lapse.
- A Geographical Dictionary, Representing the Present and Ancient Names of All the Countries, Provinces, Remarkable Cities ...: And Rivers of the Whole World: Their Distances, Longitudes and Latitudes (1688)
- Stephen, Leslie (1886). "Bohun, Edmund". In Stephen, Leslie. Dictionary of National Biography 5. London: Smith, Elder & Co. pp. 306–307.
- Andrew Pyle (editor), Dictionary of Seventeenth Century British Philosophers (2000), article on Bohun, pp. 105-7.
- Mark Goldie and Robert Wokler (editors), The Cambridge History of Eighteenth-century Political Thought (2006), p. 46.
- Tony Claydon, Europe and the Making of England, 1660-1760 (2007), p. 247 note 116.
- J. P. Kenyon, Revolution Principles: The Politics of Party 1680-1720 (1977), p. 31.
- David Hayton, Eveline Cruickshanks, Stuart Handley, The House of Commons, 1690-1715: Volume 1 (2002), p. 1066.
- Evan Whitton, Patrick Cook, The Cartel: Lawyers and Their Nine Magic Tricks (1998), p. 60.
- Charles Warren, History of the Harvard Law School and of Early Legal Conditions in America (1908), p. 109.
- Samuel Wilton Rix (editor) (1853), The Diary and Autobiography of Edmund Bohun Esq.
- Mark Goldie, Edmund Bohun and Jus Gentium in the Revolution Debate, 1689-1693, The Historical Journal, 20 (1977), pp. 569–86.
- Mark Goldie, Charles Blount's Intention in Writing "King William and Queen Mary Conquerors" (1693), Notes and Queries 223 (1978): pp. 527–32.