This is one big problem with warp drive in star trek, and most FTL drives in sci-fi for that matter. Roddenberry admitted that he had actually intended the ship to become transparent while at warp, since the vessel is moving so fast that light would not be able to keep up with it to be seen.
This however, does not really work for most audiences, so they made the ship opaque with stars streaking by.
-Although, I kind of always thought that instead of disappearing, it should be more like when you hear an airplane after it has already passed by. Maybe there is an instantaneous flash of light but by the time you see it the ship had passed by long before, and that is simply the amount of time it has taken for the light to reach your eyes or sensors or whatever. Iono I guess that wouldn't really work but it would be kinda cool.