The Stable Bridle is an item from The Legend of Zelda: Breath of the Wild. It is the default bridle that Link receives upon registering a horse at a stable for 20 Rupees. Unlike most bridles, it does not appear in the key items menu and can only be seen in the bridle selection menu when switching bridles at stables.
The only horses that do not receive one upon registrationare the Giant Horse and Epona which receive special Bridles and Saddles unique to them.