Actually, you are not far off about the service being bad and the passengers not coming again: when a new route is inaugurated, there is no way for the game to judge the waiting time, so it is assumed to be the lowest possible level (about a minute). Once routes have been running for a while, the waiting time can be fixed properly, and, that together with the journey time can make the journey too slow for all or most passengers.
As for the AI traffic - this is generated after the end of the first month, which is why you will not have seen them initially. It is based on the number of passengers in the town in which it is generated who use private cars (including horse drawn carriages in the early days). The figure 1 that you are seeing represents the percentage of people in the town with access to private cars: here, it is 1%, as, in the 18th century, only the very richest (one might say approximately 1%, although precise figures are not, to my knowledge, available) had access to their own carriages.