It depends on the construction of your drive
The acceleration of the ship in an Alcubierre bubble is due to the compression of spacetime ahead of it. It is equivalent to that of falling into a gravity well. Consider how that spacetime compression is being achieved and we can speculate as to what the view from inside would look like.
Proposals for such a drive fall into two major categories: Wormholes and Tachyons. While you don't have to be specific with your story, the mechanics would affect the shape of your light cones.
Moreover, according to Serguei Krasnikov,[19] generating a bubble in a previously flat space for a one-way faster-than-light trip requires forcing the exotic matter to move at local faster-than-light speeds, something that would require the existence of tachyons
Additionally, regarding the Alcubierre metric, there are choices to be made as well. Does spacetime unfold behind the ship or in another direction?
An extension of the Alcubierre metric that eliminates the expansion of the volume elements and instead relies on the change in distances along the direction of travel is that of mathematician José Natário. In his metric, spacetime contracts towards the prow of the ship and expands in the direction perpendicular to the motion, meaning that the bubble actually "slides" through space, roughly speaking by "pushing space aside".[9][10]
It follows that we must consider the nature of the compressed spacetime ahead of the ship. Do the geodesic lines diverge out? Only light traveling through the spacetime that is shared with the ship can be seen from the ship.
Wormholes: In this case, a spacetime fold exists (naturally or artificially) in the corridor between your ship and its destination. Light from the far end should be visible normally as you would see looking through a tube. However, you can choose whether the metric allows light to enter the tunnel through the sides or not. If so, it would probably have similar effects as Gravitational Lensing.
Tachyons: In order to fold spacetime ahead of the ship superluminally, something must trave ahead, faster than the speed of light, to deliver the energy required to compress spacetime. Here, all bets are off as tachyons are purely hypothetical and their effects are as well. Is there a Naked singularity ahead of your ship or did your drive produce an event horizon? You could make a case for seeing nothing but black, or bright white as light is distorted by the compressed spacetime ahead.
So to answer your question and give a suggestion: As others have pointed out, writing a dissertation into the story is not ideal. It requires a level of understanding from readers that is really not necessary. As all effects on light seen from an Alcubierre driven ship are hypothetical, pick one, give a short explanation, and your readers will accept it.