'Pull Up to the Bumper' was co-written by Grace Jones herself, Kookoo Baya and Dana Manno. The song's instrumental path was originally recorded in 1980 during the Warm Leatherette sessions, however, it did not make the album as Chris Blackwell found its R&B sound not fitting in the rest of the material. It was finally completed for the 1981 critically acclaimed album Nightclubbing and became its third single in June 1981. The song sparked some controversy for its suggestive lyrics, as they figuratively describe sexual intercourse, prompting some radio stations in the United States to refuse to broadcast it.