I think that KOA is about 15-18 miles east of the city. In order to get to the public transportation (city buses) you will need to get to the downtown area. You will get on the bus downtown and it will take you to the first turn of the Speedway. That would be great if you had tickets in the first turn and not so good if your tickets are in the 3rd or 4th turn, long hike to get to your seats. After the race, all of the buses are staged just outside of the first turn, when full, go to downtown and return to the staging area for another load of passengers.
To answer your question, the buses do in fact have a special route which is used by taxis, buses and escorted vehicles (10th St.). There are pluses and minuses to using these buses. You are correct that they, at a minimum, move fairly rapidly after loading. However, as previously mentioned, a lot depends on where your seats are located, weather conditions, when you get to the buses for loading.
Not sure if this is helpful but would be willing to discuss any other questions that you have.
2014 Newmar DSDP 4018-450