Whether you are referring to the Jewish Bible (the Torah plus the Prophets and the Writings) or the Protestant Bible (the Jewish Bible plus the New Testament), or the Catholic Bible (which contains everything in the Jewish and Protestant Bibles plus several other books and passages mostly written in Greek in its Old Testament), the word “Bible” must be capitalized. Remember that it is the title of a book, and book titles are normally capitalized. An oddity in English usage is, however, that “Bible” and the names of the various parts of the Bible are not italicized or placed between quotation marks.
Even when used metaphorically of other sacred books, as in “The Qur’an is the Bible of the Muslims,” the word is usually capitalized; although in secular contexts it is not: “Physicians’ Desk Reference is the pharmacists’ bible.” “Biblical” may be capitalized or not, as you choose (or as your editor chooses).
Those who wish to be sensitive to the Jewish authorship of the Jewish Bible may wish to use “Hebrew Bible” and “Christian Scriptures” instead of the traditionally Christian nomenclature: “Old Testament” and “New Testament.” Modern Jewish scholars sometimes use the Hebrew acronym “Tanakh” to refer to their Bible, but this term is not generally understood by others.