If you look carefully at the band structure of a zigzag graphene nanoribbon, it's quite complex in the area close to Z=pi/a - it's actually a big wiggly (this is shown in the tutorial). This is why T(E) at zero bias is 4 and not 2. What will happen when a bias is applied is that rather than make the conduction and valence band tangle up, as in the zero bias case, they will split and create a small gap. Actually the conduction and valence bands will attach themselves to the Fermi levels in the two electrodes, so as the bias is increased, the bands will be pulled apart by about the same amount as the bias (this is precisely what Nori wrote, just in other words).
It should be noted that applying a bias to a perfect, infinitely long ribbon is a bit artificial, and actually rather hard to describe with the kind of models implemented in ATK. A more appropriate (and interesting) case is when some defect or distortion is introduced in the central region, or when the two electrodes are different, e.g. p/n doped.
