Bridal is the adjective form of bride (a woman who is getting married). It is not the same as “wife”—a married woman—but rather a woman at her wedding, or while preparing for her wedding. The adjective bridal can refer to anything associated with being a bride:
The bridal party included the bride, her parents, and the maids of honor, her best friends.
Bridle has several related meanings. As a noun it refers to the device you put over a horse’s head, so that a rider can control the horse. It is also a verb meaning “to put a bridle on a horse”:
She bridled the horse carefully, but the bridle fell off because it was broken.
Bridle can also be used as a verb meaning “to control or hold back” or “to show anger or refusal to cooperate by pulling oneself back”:
(Control or hold back): Please bridle your tongue; you are being rude!
(Anger or disobedience): The vegetarian bridled at the suggestion of sushi for dinner.
You can see that the latter uses of bridle are based on the idea of a horse-bridle, so they should be easy to remember.