OK. Now take that thought to a logical conclusion. If the light leaving the point that you are traveling from gets from B to Earth in one year subjective to the person on Earth viewing it... Why don't you?
In other words... since time slowed down for you and it only took one year of time in your subjective timeframe - BUT it took many times that to an observer on Earth - did you really go the speed you think or did you not? And if you didn't, then what about the claims that light does?
Your close, but your a bit confused about where the time dilation happens.
If you are lobbed at a star 10 ly away at .999C or so, you will arrive in 10 years, our time. But to you you've only been traveling for a few days, hours, or even minutes depending on just how close to light speed you got.
At close enough values to c, you could cross the galaxy in seconds - from your point of view. Of course, by the time you got where you were going, even though it seemed like such a short time to you - everything will have changed. The star you were heading too might halfway around the galaxy when you get where it was. If you travel far enough the star might be even be dead when you get there.
If you missed this effect, look closer at common examples, like the clock on a spaceship one.
If we could point a telescope at a giant clock stuck on a spaceship traveling at near c, the clock would appear to be almost stopped. The second hand could take years to complete a revolution. Time passes slowly for the ship, from our frame of reference.
Of course, this is all from our frame of reference. Part of relativity is that all frames are equally valid. There is nothing wrong with the person on the ship saying the universe sped up around him, either. In both cases, 10 years will have passed 'outside' the ship, even if only seconds passed inside.
