I'm not sure I see your point. Are there not times when saying "A Bible" is correct? Example:
"There's a Bible on the bookshelf, and another on the table".
Could you clarify, please?
uncapitalized:
--> : a publication that is preeminent especially in authoritativeness or wide readership <--
The Bible is always capitalized, but when merely referencing an authoritative, widely accepted publication as "the bible" of (whatever) it's not capitalized.
Hope that helps.