A set of leather straps that are put around a horse’s head to allow its rider to control it. (Cambridge Dictionary)
The headgear used to control a horse, consisting of buckled straps to which a bit and reins are attached. (Oxford Dictionaries)
The headgear with which a horse is governed and which carries a bit and reins. (Merriam – Webster)
A bridle is a set of straps that is put around a horse’s head and mouth so that the person riding or driving the horse can control it. (Collins Dictionary)
Example
Micklem Competition

https://www.doversaddlery.com/mickelm-competition-bridle-dmo/p/X1-TR804/