I see. So when I talk about "my wife" (a proper noun, according to you), I should say, "my Wife." Or I ought to say, "I'm going to the Library." Or, "Honey, go get me that Can of Soup."
Ludicrous. Proper names, not proper nouns, are capitalized.
If we say, "I'm going to the Mayberry Library," that's a proper name. If we say, "I'm going to the library," it's still a proper noun, but no longer a proper name, and is not capitalized. In the same way, "bible" is a proper noun, but not a proper name.
The University of Maryland is wrong. I'll pit that against Phillips Theological Seminary who says that "bible" isn't capitalized.
When you go to a bookstore to buy War and Peace, you say, "I need War and Peace." When you go to buy a bible, you say, "I need a bible." Note the difference? the indefinite article "a" designates that "bible" is not a proper name that requires capitalization.