What type of bridle to you have? Does it have leather ties, chicago screws, quick release leathers, hooks...? There are so many differant bridles made so many differant ways we can't tell you with just that little information.
Its an english bridle with hooks, so your suppose to push the leather forward to release from the hook to pull it back! It took me forever to pull the leather from the keeper to start with. Perhaps it is abit dry so will use some oil on it to soften it.
If you're right handed, hold the billet in your left hand with the tab pointing to the right. Push the loop (around the bit ring) towards the hook position with your left thumb, at the same time pinching your right thumb and forefinger between the tab, where it goes over the hook, and the leather beneath. You should find it'll lift off the hook.
To replace, just reverse this ie. Thread the tab through the two keepers, position the hole and slot over the hook, press down and slide to the left. Voila!