If you're travelling at just under the speed of light, then light travels past you like a slow moving vehicle. You won't notice a change however, because almost all light sources are constant, so it'll still be a solid beam of light. You would see head or the tail the beam of light moving slowly if it were switched on or off respectively (like with a flashlight).
Again, I may be misinterpreting this, but doesn't the Speed of Light Postulate state that the speed of light in a vaccum has the same value in all inertial reference frames, meaning that light would travel 3*10^8 m/s regardless of how fast you were moving.