Why is it that light reaches you in the same time when you are still as it does if you were moving towards it?

Time dilation. The ship is moving at a significant fraction of c, and as a result time is going to be heavily dilated on board the ship. The result is that, while we would expect the speed of light as measured on the ship's instruments to be faster than c, the slowdown in time exactly compensates for the ship's speed, resulting in a measurement of c no matter how fast the ship is moving.