I think the Knight Bus engages in some sort of Apparition-like magic when it transports itself around the country.
Chairs slid backwards again as the Knight Bus jumped from the Birmingham motorway to a quiet country lane full of hairpin bends. Hedgerows on either side of the road were leaping out of their way as they mounted the verges. From here they moved to a main street in the middle of a busy town, then to a viaduct surrounded by tall hills, then to a windswept road between high-rise flats, each time with a loud BANG.
Order of the Phoenix - chapter 24 - Occlumency
I think the Knight Bus relies on Apparition, unusually fast speed for a vehicle of its size and structure, invisibility (via Disillusionment Charm perhaps?) as it seems to appear from thin air, and on the oblivious nature of Muggles, to avoid detection.
There was another tremendous BANG, and next moment Harry found himself flat on his bed, thrown backwards by the speed of the Knight Bus. Pulling himself up, Harry stared out of the dark window and saw that they were now bowling along a completely different street. Stan was watching Harry’s stunned face with great enjoyment.
‘This is where we was before you flagged us down,’ he said. ‘Where are we, Ern? Somewhere in Wales?’
‘Ar,’ said Ernie.
‘How come the Muggles don’t hear the bus?’ said Harry.
‘Them!’ said Stan contemptuously. ‘Don’ listen properly, do they? Don’ look properly either. Never notice nuffink, they don’.’
Prisoner of Azkaban - chapter 3 - The Knight Bus
Even though Harry is thrown backward for only "a moment," in a blink of an eye the bus is gone from Privet Drive and back in Wales. To me this indicates some kind of instant transportation like Apparition. Or perhaps the Portus Charm is used (Portus is what creates a Portkey) or the fundamental magic behind a spell like Portus.