Whenever someone says, "the Bible teaches" or "the Scriptures say," I either chuckle in my head or I cringe (depending on my mood). I might get caught in saying it too, but the truth is, "the Bible" doesn't really "teach" any one thing. It's really all semantics because I'm totally comfortable with saying something like "we know from Scripture..." and I am quite fond of referring to the "Biblical narrative" even in saying, for example, "the Biblical narrative teaches..." But to make such a claim as "the Bible teaches," demonstrates a somewhat less sophisticated understanding of the Bible as a whole.
The Bible, after all, is not one book. The Bible is a small library of books which all "teach" and say different things in different contexts about different topics in different genres. So it is better to say that one book teaches or another book teaches than to say "the Bible teaches." Using the term "Bible" as though it expresses one monolithic ideal or set of ideals is just not helpful and it does no justice to the complexity and contextuality of the various books in the canonical collection.
This is why, in general, I prefer the term "Biblical narrative" to express a more unifying message of the Scriptures. The beauty of Scripture is that, while it is a collection of books that give different perspectives, they all work together toward telling a story of God's relationship with the world and with our experience. The Biblical narrative is a story about a God who created the world and who refuses to give up on it until it is restored to his imagination and creative intention for it.
The difference between the Bible and the Biblical narrative is that the Bible is a collection of books which do not all say the same thing while the Biblical narrative is the underlying story that moves like a stream throughout the various texts of the Bible. Therefore, when trying to express a more unifying "Biblical perspective," we would do well to use the terms on their own terms.