Bed-Knob and Broomstick - Mary Norton

Well, not quite. A witch-in-training, Miss Price hasn't got the hang of flying on brooms nor has she learned to be properly wicked. And her spells -- well ... practice makes perfect. Yet she can't practice if Charles, Carey, and Paul reveal her secret.

To win their silence she enchants a bed-knob so that the children's bed will take them anywhere they want.

But traveling by bed is a clumsy sort of magic. The children want adventure, but what they get is trouble ... trouble of the most breathtaking, fantastic, unforgettable kind.