In The Taming of the Shrew, why does Bianca change into a "shrew" at the end?

yes you are right and that is because Katherine (when she was a shrew ) was learnt how to be tamed by Patruchio her husband... when he married her , he insisted to tame her by making the opposite of what she wanted saying that those deeds were for his love towards her ( like :shouting at the dress and hat makers declaring that their products were not good ones although they were made according to the fashion during that time)

Bianca was believed to be the tamed daughter of Baptista but at the end she proved quite the opposite by refusing to come to her husband when he ordered her to do so on their wedding day thus her husband said :"I wish your duty were as foolish too!The wisdom of your duty,fair Bianca, has cost me a hundred crowns since dinnertime."

So Patruchio was right and Katherine was a good lady and maybe her shrewish character was because she didn't know how to improve it while Bianca's character was a bad one hiding itself behind  untrue  words.

Moral lessons: we must compare between promises and actions ,,, live in peace & love eachother  to lead a quiet life.