Bartlett was of an old-established quaker family at Bradford, Yorkshire, where his father was an apothecary, having for his apprentice the afterwards celebrated Dr John Fothergill.
He left Bradford for London, where he set up an apothecary's business in Red Lion Street.
This, however, he was eventually obliged to relinquish on account of failing health, resigning it to his partner, Mr. French.
His only literary venture was a memoir on the Episcopal Coins of Durham, and the Monastic Coins of Reading, minted during the reigns of Edward I, II, and III, appropriated to their respective owners, this having been the substance of a paper read before the Society of Antiquaries on 5 March 1778.
He died of dropsy on 2 March 1787, at the age of 73, and was interred in the quakers' burying-ground at Hartshill, Warwickshire.