It does not involve turning into the ball, even though that seems a good strategy, it just won't get you high enough.
Take the powerup and activate it, but don't fly up. Wait for the powerup to respawn and pick it up a 2nd time. Now fly up one or 2 screens, quickly disable the powerup and reenable it. Now you should be able to fly all the way up. Try to guess how long you can delay to reactivate the powerup. The longer you can do that, the higher you can get.