A 19th/early 20th century illustration: “The Passing of the Vestals” (stylized). Here, two Vestals are seen riding along a street in Rome in a two-horse chariot as people bow to them.
The streets of Rome, especially in the fora, were so busy that most people weren’t allowed to ride in carriages or chariots. This mode of transport was reserved for important people only. The type of chariot depicted here is called a carpentum: along with triumphant generals and other men and women of unusually high status, the Vestals were permitted to travel in them. They were similarly allowed to travel in lecticas (a curtained couch of sorts carried by porters) and were always given the right of way.