Light, apart from a photon, is a wave. Brandon has mentioned somewhere that if something is half in, half out of a speed bubble, wether it is sped up depends on how said object sees itself. The way I see it is this. When the light sees itself as inside the speed bubble, the whole beam is suddenly incorporated at the same time. Now, as mentioned in the main post, the speed of light is constant. either the light sees itself as completely out of the bubble, or it progresses inside the bubble, entering the bubble instantaneously, without crossing any sort of 'boundary'. This would mean no red shift.
That's how I always saw it, at least.