He reportedly wrote the song while sick in bed during the group's week-long engagement at Bournemouth in August of 1963. Bill Harry of Liverpool's Mersey Beat paper had been urging George to try his hand at songwriting and so, worn down by Harry's insistence and with time on his hands, he came up with Don't Bother Me. Now, he simply had to convince producer George Martin, manager Brian Epstein and music publisher Dick James to allow him to record his maiden composition with the greatest act in British show business history.
September 11th was the next recording date scheduled for the album-in-the-works. The band recorded four Lennon-McCartney songs before turning its collective attention to Harrison's number late in the evening session. According to Dave Rybaczewski's in-depth look at the song, John took up some time trying to play his rhythm guitar through a new toy called a fuzz box before Martin nixed the idea. This immediately established the lack of focus that John would display toward George's compositions throughout the coming years. Four takes of the backing track and three of overdubs yielded unsatisfactory results for the time being.
They returned to the number at the start of the evening session on the following day, September 12th. Beginning with the round number of take ten, they tried a few different arrangements before hitting the right one on take thirteen (you can even hear George say "Too fast" during the intro on the record, but he obviously changed his mind upon hearing it). Several takes of overdubs brought the total to take nineteen, but the best overdubs were from take fifteen. These included George double-tracking his lead vocal, Paul on claves, John on tambourine and Ringo on a loose-skinned Arabian bongo (as detailed in Tony Barrow's liner notes for the album).
Young Mister Harrison had learned his new craft well enough to land his number on side one of With the Beatles among those of the hottest songwriting team working at the time. A few months later, Capitol Records placed it prominently at the top of side two on the breakthrough American album Meet the Beatles. Though the group never played it live, Don't Bother Me was chosen to be one of three songs used in the discotheque sequence in the film A Hard Day's Night.