Whiter than white

In the early scenes of the play, Bianca is characterised as a pretty, obedient and polite daughter who lives up to her name (‘white’) in looks and character. When Lucentio first sees her, he is particularly struck that she is ‘young and modest’, ‘sacred and sweet’. Bianca is thus a direct contrast to Katherina and thrives on the consequent attention she gets from her father and from other men as an eligible marriage partner. The true daughter of a patriarchal society, Bianca is apparently happy with being controlled by the men around her and plays up to it with overtly ‘feminine’ behaviour. In Act 2 Scene 1, her submissive attitude infuriates Katherina as she says:
Or what you will command me will I do,
So well I know my duty to my elders.
Act 2 Scene 1     
Bianca knows that her father, Baptista, will take her side in any quarrel with the physically stronger Katherina and plays on this with her tears and her meekness, both of which Katherina perceives as fake. 

The beloved prize

Bianca is clearly physically attractive and draws the eyes of myriad suitors, who overlook Katherina. She is described as ‘Beautiful Bianca (Act 1 Scene 2) with her ‘fair’ face and ‘coral lips’ (Act 1 Scene 1). Enjoying the favour of many suitors, she does not have to be married until Baptista has found a husband for Katherina and so can be choosy: ‘I’ll not be tied .. / But learn my lessons as I please myself’, (Act 3 Scene 1). 
Until she meets Lucentio (in disguise as her Latin tutor), Bianca has the luxury of not yet having to seriously consider marriage. Even when she meets the man who wins her, she is wise enough to be circumspect, as her coded message to Lucentio demonstrates: ‘I know you not;.. I trust you not; .. presume not;’. However, there is a suspicion that, for all her demureness, Bianca enjoys her power over men and is a flirt. The end of her message to Lucentio/Cambio is an enticing ‘despair not’ and, on observing her, Hortensio is soon suspicious of her ‘wandering eyes’/fickleness (although this may say more about Hortensio’s jealousy than about Bianca).

No moral dilemma

In Bianca’s relationship with Lucentio, with whom she quickly falls in love, Shakespeare draws on the characterisation typical of the ‘young lovers’ (Gli inamorati) from the Italian Commedia dell'Arte tradition. These characters were lovers of high status who faced the dilemma of either following their hearts or being obedient to the wishes of their parents. In The Taming of the Shrew, this is the dilemma which reveals Bianca’s true colours.
Bianca has no qualms about conducting her relationship with the disguised Lucentio behind her father’s back. It is clear that Bianca does not care about her reputation, other than its appearance, and has decided who she will marry whether or not she has her father’s good will. Meanwhile, her dismissive treatment of the music tutor (Hortensio/‘Litio’) reveals a callous side to her character. When Katherina is dragged away from her own wedding breakfast, Bianca appears to regard her sister’s plight with cynical amusement: ‘being mad herself, she’s madly mated’ (Act 3 Scene 2).

A whitewash

By the end of The Taming of the Shrew, Bianca compares unfavourably to Katherina. Not only has she exerted her independence to marry in secret, in a way that undermines her father’s position in society, but she is also contemptuous of her new husband’s ‘headship’. It seems ominous that she is already ‘conferring by the parlour fire’ with the cantankerous Widow (Act 5 Scene 2). 
The hypocrisy of Bianca’s covert manipulation is apparent in her reaction to her husband’s confident wager, with an open insult and implied warning: ‘The more fool you for laying on my duty’ (Act 5 Scene 2). No longer acting in the shadows, Bianca reveals an aspect of her character which perhaps only Katherina had known was there at the beginning of the play.
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