Apple wrote "Paper Bag" following an experience in which she mistook a paper bag for a dove. The event took place in Los Angeles following recording sessions for her previous studio album, Tidal (1996); Apple, reportedly upset at the time, was a passenger in a car being driven by her father.

Allmusic's Matthew Greenwald described "Paper Bag" as having a "loose, almost ragtime" melody and rhythm pattern, with an "up and down" chord pattern creating a "funky, looping feel".The Record noted the "infectious" song includes "Beatlesesque horns".The Boston Globe classified it as a "piano ditty" that "owes equally to Kurt Weill and Paul McCartney," while The Buffalo News noted that it "provides a more contemporary hip hop sound" than other songs on her album.

Matthew Greenwald of Allmusic wrote that "Paper Bag" was one of the more accessible, "inspiring" tracks from the album. Greenwald appreciated Don Sweeney's horn arrangement, which he called "joyous". In 2012, Bob Gendron of the Chicago Tribune opined, "A midst a backdrop of gently brushed drums, 'Paper Bag' highlighted an ugly tempestuousness at odds with its breezy cabaret melody." In the "Rolling Stone Special Nineties Edition," the song was ranked as the 29th best song of the 90's.

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