The practical employment of the day broomed away fantastic cobwebs.
Old English brom "broom, brushwood," the common flowering shrub whose twigs were tied together to make a tool for sweeping, from Proto-Germanic *bræmaz "thorny bush" (cf. Dutch braam, German Brombeere "blackberry"), from PIE root *bh(e)rem- "to project, a point."
Traditionally, both the flowers and sweeping with broom twigs were considered unlucky in May (Suffolk, Sussex, Wiltshire, etc.). The witch's flying broomstick originally was one among many such objects (pitchfork, trough, bowl), but the broomstick became fixed as the popular tool of supernatural flight via engravings from a famous Lancashire witch trial of 1612.
To run or walk away, esp to escape by running (1800s+)