A bridle is a piece of equipment used to direct and control a horse. The bridle includes the headstall (that goes around the horse's head) and holds a bit that goes in the mouth of a horse, and also the reins that are joined to the bit.
A headstall without a bit uses a noseband to control a horse, is called a hackamore, or a bitless bridle. There are many different designs with many different names, but all use a noseband that puts pressure on sensitive areas of the animal's face in order to provide direction and control.
A bridle as said in a dictionary is a piece of equipment that helps contral a horse.
In the poem "The Man From Snowy River" by Banjo Paterson it says "He never drew the bridle till he landed safe and sound," This is talking about the same thing.