Just to take a simpler route to answer this question all in good fun, I would say that Bianca isn't a shrew at the beginning but becomes one in the end because she is a dynamic character and was designed to be that way by Shakespeare.  Although some critics disagree with me, I think of Bianca as a sort of foil to Katharina.  They go through their dynamic changes directly opposite of each other:  Katharina turning from shrew to loving female and Bianca turning from loving female to shrew.  I have to admit, though, I don't usually describe Bianca as a "shrew" at the end of the play.  Still, anger can certainly make a lady quite ugly, can't it?  Therefore, in speaking of Bianca as a shrew, I suppose that if the shoe fits, ...

Kathrine is considered the shrew in the title because she refuses to be ruled by her father.

In Kathrine's world, her father would choose her husband.  Love was not a part of the equation.  What was important was a "good" marriage.  Family connections and how much money was involved were also all important.  It is a male dominated world and Kathrine wants nothing to do with it all.

Bianca, on the other hand trusts that her father will marry her to the man she wants since she has him wrapped around her little finger.  Once she gets what she wants she doesn't have to pretend any more.  She shows her true colors.  (Her name means white.)  In a sense, she has been dishonest whereas her sister has been honest to a fault.

Basically, Kathrine rebels against the male dominated world she lives in whereas Bianca submits to it.

Good question. Since we aren't told this directly, we must deduce our answer from the action of the play. I would say it is because of three things. First, the focus has shifted. She was the good one, and Kate so shrill that no one could see her beauty. Now that Kate is good, her beauty is visible, and Bianca is mad. Second, the structure has shifted. They aren't both competing for their father's approval and that of unmarried men; they are showing off as wives, and the criteria are different. Third, Petruchio is more impressive in the end than her husband, and some of that glory reflects.