He was born to Samuel Bosanquet, the governor of the Bank of England, and his wife Eleanor, and was educated at Eton College before being accepted into Christ Church, Oxford.

Before his call he had, with Christopher Puller, started the Reports of Cases argued and determined in the Court of Common Pleas and Exchequer Chamber, and in the House of Lords.

[1] He was made a Serjeant-at-Law on 22 November 1814, and from that time came prominently before the public in the numerous bank prosecutions which he conducted with great discretion for thirteen years.

Upon the resignation of John Copley, 1st Baron Lyndhurst, Bosanquet in conjunction with Charles Pepys, 1st Earl of Cottenham, the master of the rolls, and Sir Lancelot Shadwell, the vice-chancellor, was appointed a lord commissioner of the great seal.

[1] He retired from the Common Pleas in 1842 due to ill-health, and died on 25 September 1847 at Firs, Hampstead Heath.