Book about a girl learning to be a witch

Question

Looking for the name of a children’s book where a little girl is taught to be a witch. What’s striking is that they ride the broom the other way around and the progs of the broom guide the broom. The book cover was purple. There was no family she just went to some shop dressed as a witch in a rubbish bag and the owner is an old lady and she trains her to be a witch That’s about what I remember about the story. My daughter read it as a 5 year old in 2002

Answer 1

How about Ruth Chew's Witch's Broom?

Amy's mother found the little broom in their back yard, near the peach tree. It didn't sweep very well. But Amy and her friend Jean found it could do other things—and one of the things it could do was fly!

With the further details, and the content of this review, this is looking less likely, but it's a start.

Answer 2

It’s Flying Lessons (2011) by Maeve Friel, the first book in the Witch-in-Training series.

From Goodreads:

The first in a new series of magical books for younger readers, by Irish author, Maeve Friel. Jessica thinks she is an ordinary ten-year-old girl but by the end of this first book, she is on the way to becoming a very bright young witch! When she sees the broomstick for sale outside Miss Strega’s hardware shop, Jessica is intrigued. for on the price label it also says: Flying Lessons Extra. Jessica can’t resist peeking inside the shop and ends up beginning her first lesson in witchcraft. Jessica learns that there is more to learn about flying a broomstick than meets the eye. First, you have to use the branches as gears – so the twigs must be in front of you, not behind you as every other witchy book show. The foremost twigs are for twirling, zooming, spinning, ducking, diving, moon-vaulting, and star falling. The Eject twig, is for getting rid of unwanted hangers on, Goblins, dragons – any sort of pest that tries to hitch a ride. Join Jess as she works towards her Flying Certificate and becomes a GASP of BR[EATH] in order words, a Graduate Airborne Spinner of Broom Riders [Earth and the Heavens]!

Answer 3

Carbonel: King of Cats by Barbara Sleigh is a match plotwise, but none of the covers show them riding backwards.

Rosemary's plan to clean houses during her summer break and surprise her mother with the money hits a snag when an old lady at the market talks her into buying a second-rate broom and a cat she can't even afford to keep. But appearances can be deceiving. Some old ladies are witches, some brooms can fly, and some ordinary-looking cats are Princes of the Royal Blood. Rosemary's cat ("You may call me Carbonel. That is my name.") soon enlists her help in an adventure to free him from a hideous spell and return him to his rightful throne. But along the way Rosemary and her friend John must do some clever sleuthing, work a little magic of their own, and—not least— put up with the demands of a very haughty cat.