Bridal is related to a bride, but bridle refers to a part of a horse's harness and what you do with it. Although the words sound the same, they run in different circles unless you're getting a horse ready for her wedding.

Bridal refers to something to do with a bride or a wedding. It comes from the Old English word brydealo for wedding feast. It's formed from bryd, for bride, and ealo, or ale, which was often drunk at wedding feasts. Here's bridal in the news:

There are bridal trends that will never go away, such as the classic white gown and the big balloon skirt. (ABC News)

Forgo the champagne treatment a bridal boutique often provides. (Associated Press)

"I wanted nothing bridal, nothing white," Mr. Alexandre said. (New York Times)

The word bridle also comes from an Old English word, meaning "to move quickly."  Used as a noun, bridle is part of a horse's harness. As a verb, it can be used to mean restrain, as you would a horse in its bridle. If you bridle at something, you're angry or offended.

Before the tent sits a cavalier, glass in hand and holding a horse by the bridle, talking to a woman standing in front of him. (Esther Singleton)

As a result, I instantly bridle at news the government could sell off these beautiful and therapeutic spaces in search of a quick buck. (BusinessGreen.com)

You can think of this form of bridal as bride + -al, and all of the stuff that goes with a wedding, but bridle is the thing that restrains a horse, and what you might do if someone tried to put a leather harness on your head.