The only time I have had issues with things going "missing" is when I was at a barn with some younger kids who liked to "borrow" what they didn't have or wanted. :-S
I agree that a talk with the BO and a note or sign will probably bring the bridle back and if it doesn't I would discuss with the BO about the possibility of doors/locks being put on the lockers to keep this from happening again, as it was either a honest mistake, or borrow and you will get it back or sadly there is likely someone with sticky fingers and you don't need more stuff taken
I know a lady who embroidered all her blankets with large hot pink initials to keep people from "borrowing" them as she had that issue when boarding, she also made sure to buy all brightly colored supplies and initial them so you could see them "walking" away she said it worked well!
I hope you find it! Remember to check all the places you know it isn't