Is there any way to avoid the blue-shell in Mario Kart 7?

Right before a Blue Shell hits you, it stays stationary in the air for a split second before falling down and hitting you. Because of this, you can use a Mushroom to dodge one if you time it just right. This was easier to do in Mario Kart Wii than in Mario Kart 7, due to changes in the Blue Shell's mechanics, but it is still possible, as illustrated by this YouTube video.

(Of course, you could also use a Star or Bullet Bill before the impact of the Blue Shell, which would also result in your dodging it.)