I would it up really good with glycerin soap or a regular leather cleaner. I would then use a really good conditioner on it to hydrate the bridal so it's not so dry and hard to bend. Do this for about a week, maybe less, and it should come back to life!
Hope this helps!
Just clean it good! I personally would avoid oils because in my past experiences I have had the leather break afterwards. I would just wipe it down and maybe scrub with leather cleaner and maybe add a touch of conditioner (not oil)