In the Prologue, Chaucer writes of the Wife of Bath, "At making cloth she had so great a bent / She bettered those of Ypres and even of Ghent" (lines 447-448). The Wife of Bath works in business for herself as a cloth maker, so she is of the merchant class. She has been married and widowed five times, and only a widow in Chaucer's time was allowed to own her own business. There is the following description of her clothes: "Her kerchiefs were of finest weave and ground; / I dare swear that they weighed a full ten pound" (lines 453-454). The Wife of Bath wears fine hats that weigh ten pounds, and she wears hose that are scarlet in color and shoes that are new. Her hats are broad, and she wears a rug across her bottom. From her elaborate clothes, we can gather that she has done well for herself in business. She travels widely, including to Rome and Jerusalem, and she clearly enjoys independence and luxuries. Therefore, she is a wealthy person who has made her money in business.
Alisoun, the Wife of Bath, is a wealthy middle-class woman. Although in the United States, we associate wealth with being upper class, in medieval Britain (as today), to be in the upper classes one's family had to be aristocratic (or a royal), which meant deriving their income from a landed estate. In contrast, Alisoun's wealth comes from cloth making and marriage.
A mark of an upper-class woman was that she did not work outside the home to earn money, as Alisoun does. Alisoun also has no title, such as "Lady," in front of her name to indicate an aristocratic heritage or marriage. Her way of speaking is down-to-earth and characterized by common sense. She does not use the courtly language associated with aristocrats. Finally, we know she's not lower class because she wears costly clothes and has traveled all over on pilgrimages. She is a woman who has had to live by her wits and earn her living by her work.
The Wife of Bath is considered to be in the middle-class group of Pilgrims. This is because of her exploitative behaviors and her attitude that a woman rules. She had five husbands and dominated each of them, the last one being half her age.