"Don't Bother Me" is the first song written by George Harrison to appear on an album by English rock group the Beatles. The upbeat rock and roll song originally appeared on the group's With the Beatles album in the United Kingdom, released in 1963, and on their Meet the Beatles! album in the United States, released in 1964.

Harrison wrote the song while ill in bed at a hotel room in Bournemouth, England, where the Beatles were playing some shows during the summer of 1963. He considered it an exercise in whether he could write a song, later saying, "at least it showed me that all I needed to do was keep on writing, and then maybe eventually I would write something good." Harrison received a writing credit for two earlier songs, "In Spite of All the Danger" (McCartney/Harrison) and "Cry for a Shadow" (Harrison/Lennon). Both were recorded by The Beatles but neither was released officially by the band until 1995's Anthology 1 compilation. Because the former was largely a McCartney composition (Harrison received a credit simply for playing the guitar solo) and the latter was an instrumental pastiche of the Shadows, "Don't Bother Me" is considered Harrison's first song by most (including the composer himself). Harrison did not think highly of the song, not mentioning it in an otherwise comprehensive overview of his Beatles compositions in his autobiography I Me Mine. The Beatles never performed it live or at any of their BBC sessions.

After "Don't Bother Me", it was not until 1965's Help! album that any more Harrison-penned songs (“I Need You” and "You Like Me Too Much") would appear on record. "You Know What to Do" was recorded in 1964, but was not released at the time.

...
Wikipedia