When you fold subspace you're not folding it across the universe, only immediately surrounding your ship. Specifically, if I'm remembering the mechanics right, you're altering subspace to create a high-density bubble behind you and a less dense bubble ahead of you. The result is that the ship is drawn forward by the low-density bubble and pushed by the high-density bubble. The reason why the result is PERCEIVED faster than light travel by an outside observer is because of relativity. The ship never actually accelerates beyond the speed of light, but because of the interaction of the low-density subspace bubble with normal space-time, the ship reaches its destination at a much higher velocity than would be possible even though PRACTICALLY the ship is not traveling any faster than it would in normal space (think of it as taking a cutoff, rather than a road that loops around).
The beauty of this mechanism is that, if the theory is correct, there will be no effects of time dilation. If you leave earth on March 5th, 2010 at 9pm and make a five-hour trip in this manner, your clock and the clock of an observer back on earth will still be synchronized at 2AM March 6th when you arrive at your destination. Whereas if a craft travels at relativistic speeds (accelerating to a significant fraction of the speed of light within normal space-time) your clock may show only 5 hours passing, but to an outside observer 5 YEARS (if not more) might have passed.