He was born on 18 June 1783 at Kirkby Lonsdale, three years before his brother Edward Bickersteth.
By the advice of his uncle, Dr. Robert Batty, in October 1801, he went to Edinburgh to pursue his medical studies, and in the following year was called home to take his father's practice in his temporary absence. Disliking the idea of settling down in the country as a general practitioner, young Bickersteth determined to become a London physician. With a view to obtaining a medical degree, on 22 June 1802 his name was entered in the books of Gonville and Caius College, Cambridge, and, on 27 October in the same year, he was elected a scholar on the Hewitt foundation. Owing to his intense application to work, his health broke down after his first term.
A change of scene being deemed necessary to insure his recovery, he obtained, through Dr. Batty, the post of medical attendant to Edward, fifth earl of Oxford, who was then on a tour in Italy. After his return from the continent he continued with the Earl of Oxford until 1805, when he returned to Cambridge. At this time he wanted to enter the army, but his parents disapproved. After three years he was senior Smith's mathematical prizeman of his year (1808), Miles Bland, Charles James Blomfield and Adam Sedgwick being among the competitors. He graduated senior wrangler from Gonville and Caius College, Cambridge in 1808 and after training as a physician like his father, he turned to law.
Having taken his degree, Bickersteth was immediately elected a fellow of his college, and thereupon made up his mind to enter the profession of the law. On 8 April 1808, he was admitted to the Inner Temple as a student, and, in the beginning of 1810, became a pupil of John Bell, and was called to the Bar on 22 November 1811.
Bickersteth became a King's Counsel in 1827, and 1836 brought him membership of the Privy Council, appointment as Master of the Rolls and a peerage, which he accepted on condition that he could concentrate on law reform and remain politically independent. He was created Baron Langdale, of Langdale in the County of Westmoreland on 23 January 1836.
He was determined that the government should provide an adequate Public Record Office and became known as the "father of record reform". As Master of the Rolls he was in effect Keeper of The Public Records. After the Public Records Act of 1838, he and his Deputy Keeper, Francis Palgrave, the full-time working head of the office, started to organise the transfer of state papers from the Tower of London, the chapter house of Westminster Abbey and elsewhere, to one single location.
In 1850, ill health forced him to turn down the chance to become Lord Chancellor and he died the following year, on 18 April 1851, at Tunbridge Wells.
He married Lady Jane Elizabeth Harley, daughter of his patron the Earl of Oxford by licence on 17 August 1835, in St. James, Paddington, London. They had one daughter, Jane Frances, christened 12 March 1837, in London.