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.