Books of the Bible - underlined?

Generally speaking, titles of books (or articles, films, etc) should be italicized. If you're writing by hand, then underline because it is problematic to italicize handwriting. Is it the same for books of the Bible? I'm not sure. The term "The Bible" is generally written with capitalization but no italicization. I almost feel as if the same applies for the books that comprise the Bible. This is because when you say "The Bible" or "The Book of James," you aren't talking about a title in the strict sense. Paradigmatically speaking, "The Book of James" isn't a proper noun but a sort of a priori label that connects this particular book with some dude named James. If James' book had a title, then you'd italicize that, but i think it would be strange to italicize "The Book of James" as though it were a title. Just capitalize the first letters (since you are, after all, refering to this particular book that enough people have deemed to be important enough to capitalize when refering to it).

Names of books of the Bible are almost invariably rendered just as any proper noun, ie no italics, inverted commas etc.

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Is the actual title of the Bible italicized if you're speaking of it in a scholarly context?

No you dont