Dibdin was the son of Charles Dibdin, a song-writer and theatre manager, and of Mrs Davenet, an actress whose real name was Harriet Pitt. He was apprenticed to his maternal uncle, a London upholsterer, and later to William Rawlins, afterwards sheriff of London. He summoned his second master unsuccessfully for rough treatment; and after a few years of service he ran away to join a company of country players. From 1789 to 1795 he played all sorts of parts; he worked as a scene painter at Liverpool in 1791; and during this period he composed more than 1,000 songs.
His first work as a dramatist was Something New, followed by The Mad Guardian in 1795. He returned to London in 1795, having married two years before; and in the winter of 1798-99 The Jew and the Doctor was produced at Theatre Royal, Covent Garden. From this time he contributed a very large number of comedies, operas, farces, etc., to the public entertainment. Some of these brought immense popularity to the writer and immense profits to the theatres. It is stated that the pantomime of Mother Goose (1807) produced more than £20,000 for the management at Covent Garden theatre, and the High-mettled Racer, adapted as a pantomime from his father's play, £18,000 at Astley's.
Dibdin was prompter and pantomime writer at Theatre Royal, Drury Lane until 1816, when he took over the Surrey Theatre. This venture proved disastrous, and he became bankrupt. After this, he was manager of the Haymarket Theatre, but without his old success, and his last years were passed in comparative poverty. In 1827 he published two volumes of Reminiscences; and at the time of his death he was preparing an edition of his father's sea songs, for which a small sum was allowed him weekly by the lords of the admiralty. Of his own songs, "The Oak Table" and "The Snug Little Island" were popular at the time.