The first time a witch rode a broom in popular culture could have been in the illustrations of a book published in 1451. French poet Martin Le Franc’s Le Champion des Dames (The Defender of Ladies) shows two women flying with sticks between their legs, although only one is clearly a broom. At least, that is the oldest evidence we have of the legend of witches flying on brooms.
According to Witchcraft in Europe, 400-1700: A Documentary History, edited by University of Pennsylvania history professors Alan Charles Kors and Edward Peters, Le Champion des Dames has “the first such illustration in the pictorial history of witchcraft.” Le Franc’s long poem about virtuous women is interrupted by a discussion of witchcraft, and the covered heads of the two women marks them as Waldensians. This Christian movement emerged in the 12th-century. With its tenet that any member could be a priest, even a woman, and perform sacraments and preach, the bloody ire of the Catholic Church soon followed. That these heretics would also meddle with the supernatural was not a leap, but why the broomstick?
What people said about witches and what they did with their brooms is pretty suggestive, if not downright prurient. Read more about witches and their brooms at Hyperallergic. Link contains some art nudity.