The patch is good. 

I was first surprised by the fact that e.characters_written is not used
in the write() method; but _flush_unlocked() already adjusts the
_write_buf according to the original e.characters_written raised by the
underlying raw file. Everything is fine.

I suggest however to add some tests around the first "except
BlockingIOError". This would answer the question:
    # XXX Why not just let the exception pass through?
For example, I modified a function in your patch:

    def testWriteNonBlockingOverage(self):
        raw = MockNonBlockWriterIO((-1, -2))
        [...]

        # Subsequent calls to write() try to flush the raw file.
        try:
            bufio.write(b"x")
        except io.BlockingIOError as e:
            # Two more chars were written at the raw level
            self.assertEqual(bufio._write_buf, write_buf[2:])
            # But write() did not accept anything.
            self.assertEqual(e.characters_written, 0)
        else:
            self.fail("BlockingIOError not raised")