Did the Wife of Bath choose her headwear out of a sense of modesty?
The Wife of Bath chose her headwear to show off her skills at making cloth. At any rate, modesty doesn't figure into her character. She was quite proud of all she was and all she'd done. She was upset if anyone in the parish made an offering before she did (or greater than she did): "In all the parish there was no goodwife / Should offering make before her, on my life; / And if one did, indeed, so wroth was she / It put her out of all her charity" (449-53). (Enjoy the play on words: Giving offerings is an act of charity, but if someone outdid her, they "put her out of all charity," meaning they provoked her envy and anger.)
The rest of her dress gives you a clue about her "modesty," as well: "Her kerchiefs were of finest weave and ground; / I dare swear that they weighed a full ten pound" (453-4), suggesting that she wore the fanciest headwear she could produce. Further, "Her hose were of the choicest scarlet red, / Close gartered, and her shoes were soft and new." Quite the opposite of modest--she dressed to be noticed.