This is pretty weak. Etymologically, the word “bible” (lower case) also means any book that is authoritative in its subject. When referring to the sacred text, it is either capitalized or even prefixed by a capitalized “The Bible”.
So, two spellings are legitimate, so no spell correction.
bible (lower case) also means any book
I have called the blueprints we use at work “the bible”. If they are wrong, we are hosed.