Uh huh..."very highy accurate", and "without errors in measurement"....those terms are scary.

So, I am human, so I have to take your word for it that if the bus goes fast enough, time stops?
IIRC, if matter were to exceed the speed of light, it is supposed to be converted to energy....
Now, can it complete that transition if time stops?
So, if the bus can't actually GO faster than the speed of light, because time slows at it approaches it, and therefore could stop if one reached it, etc...then, matter could never actually turn into energy.
Movement is relative to distance and time....if time stops, can there still be movement?
What would the bus's speedometer say if time stopped....it was was JUST about to say the speed of light...and, then, what?
I suppose headlights on a bus that can go that fast would be somewhat pointless....as the bus would be essentially keeping up with its beams.
I wonder if we turned the bus around, and drove ~ at the speed of light in reverse, if it would appear to us that the headlights beams were merely anchored at some point behind us, and grew longer towards us as we drove away?
If we drove in reverse FASTER than the speed of light, would the beams behind us be invisible to us?

What if matter flying at near light speed, from another distant big bang, flying parallel to our near light speed course, were to pass us...could we see it, or would it be invisible, as it was - to our view, going by at about double the speed of light?
As we must have an infinite number of big bangs occurring across the entire space system, stuff like this must be flying by all the time....and, I'm sure, colliding as well.
For all we know, the passing of this across us creates the equivalent (Not literally, the equivalent/analogous) of a static electric charge related to mass...and that's all we call gravity...and why mass seems to attract mass, etc.
This may have even started before busing.

So - I'm sure gravity does some odd things, heck, just playing with magnets can keep me amused for quite a while...but, time....no, don't buy it.....its not a real thing....its just a concept.
I still do not think that time will slow, speed up, or in anyway be impacted, by the objects speed through it...
I could understand if matter broke down into energy...that has plausibility, just like early planes broke apart when they hit the sound barrier...matter may break apart when the speed exceeds the cohesive forces that render it as matter.
So - the matter may be now energy...but, I can't see how an imaginary construct would be impacted by the transformation.
I agree that a GPS works....mine does, its great.

It relies on those geosynchronous satellites to say what time it is, over and over again....and for my GPS unit to say, hmmmm....look at what time it was when # 12 sent the message compared to the others, we must not be in Kansas anymore, etc.
And yeah, they degraded the accuracy so only those needing to kill someone would be able to take FULL advantage....Geochashing WOULD be less challenging if the signals were allowed to be as accurate as they could be without a secret decoder ring.

But, the time the satellite sends is fed into a computer that knows how far away that satellite was supposed to be...and essentially triangulates its position, based upon how far it is from each satellite, etc...
If two buses in space, traveling towards each other, each at near light speed, were to crash head on....they probably would not have seen each other's head lights approaching....(I suppose hitting the horn would be equally, if not more pointless...)...the particles would collide at ~ double the speed of light....
Now, as motion is a relative term, it seems logical that the relative motion of the particles hitting each other at double the speed of light might turn each other into energy....
At a minimum, the insurance would likely write them both off as complete losses, unless the company counts the energy created vs the matter destroyed...complicating the deductable, etc.
Now, of course I was a bit tongue in cheek about spacing curving back upon itself as the ultimate rounding error, but, my point is that telling me I have to believe something because there are forces at play greater than a human can comprehend hits a nerve.
I believe we can eventually understand everything, or, as is most likely, every thing will be eventually understood by at least someone....but no one will ever individually understand everything.
I also believe that there is no beginning, and no end to space....its just never ending in all directions PLACE, that may or may not be populated by stuff at any given point, at any given time.
I also believe that time is not a thing that can be acted upon...it is analogous to space, its merely the chronological space things occur within...but, it passes, whether or not anything happens...
Its just a way to refer to when something occurred.
We do NOT even have a universal clock...one that would agree with another big bang's inhabitant's clock....we can say, well, this atom will be the same, and it vibrates at this frequency very accurately, etc....
That's nice, but I think the point was made that we really do not even know which way we are moving, except relative to other objects we can detect - and there are seeming more that we cannot detect, that we can detect.
If there are other buses going by us, we probably can't even see them, unless they hit something.
So gravity can't warp time, maybe the perception of it, maybe the measurement of it...but its not a thing to be acted upon, it is merely a construct.