Because Jason didn't have a soulbond he could ride, he had to order a shuttle.
There were two different kinds of lanes inside Jiro-City and Cyro-City.
One lane was used by mana-operated vehicles like cars, trucks, motorcycles and they had a strict speed limit inside the city, while the other lane was used by soulbonds as a means of transportation, and even flying beasts could be used inside these lanes.
These beast lanes didn't have a speed limit because beasts had faster reflexes and could avoid bumping into each other easily. The width of the lanes was also much larger than those designated for mechanical vehicles.
While Greg could ride on Taurus, Malia mounted on her Nightmare-horse and their speed was extremely fast given the leveled roads.
Most people living in higher grade cities would use their soulbonds as a means of transportation and it was much faster and convenient than riding a shuttle.