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.)
There is one way that I have dodged a blue shell before, and that is hitting it with a red or green shell. If there is a straight segment of track ahead, and the blue shell is coming, you can hit the blue shell with a red or green shell by sending it behind you a little after you hear the blue shell alarm. This works because, unlike Mariokart DS, the blue shell travels on the ground until it gets close. By timing it right and getting lucky, you can avoid being hit by the blue shell. This method may probably be easier to do than the mushroom method, because if you are more likely to get a green or red shell when in first, instead of a mushroom.