This story is based on a true gift from one king to another in the 13th century. A female "ice" bear is given to the King of England for his royal menagerie, but she's restless and won't settle or eat before leaving Norway.
Arthur, who's run away from home and taken to stealing just to eat, ends up getting caught and pushed into her cage by a mean brute. But instead of eating him, she settles, and the doctor responsible for making sure she reaches England convinces Arthur to accompany her on the journey.
Along the way, Arthur is bullied by a sailor, the ship is attacked by pirates and she kills them, and the ship runs afoul of a reef in a storm and he sets her free. She defends him from bullies on land, but in the end, she's recaptured, delivered to England and separated from Arthur. She quickly languishes, and Arthur's brought back to help her find a will to live -- by swimming in the Thames in the winter.
The author's note at the end is fantastic, explaining there actually was a polar bear in the King's menagerie in the 1250s, and it was allowed to swim in the river on a tether, and its keeper swam with it, in a special, padded suit.