Does the tale the Wife of Bath tells correlate with her personality?
Yes. The wife of bath's tale correlates quite well with her personality and experience as a five time wife. She has a very dominating personality, and it is evident that she desires power over her husbands and lovers. If not power over them, then at least equal power and say in the relationship.
Her tale involves a knight who is forced into a quest to find out what women truly desire. He eventually finds out the answer to the question, returns to give the message, and his life is spared. The answer to the question of what women really want is autonomy and power over their husbands and lovers.
"What women most desire is sovereignty
Over their husbands or the ones they love,
To have the mastery, to be above.
Her story meshes quite well with her personality, because she frequently breaks her narration with information about her husbands. It's clear that she is a very controlling woman in her marital relationships.