It sounds like you need a wireless solution that will work over a short range so that there is no risk of the signal being detected at the next or previous bus stop.
But the range is unlikely to be short enough to prevent the signal being picked up at the bus stop across the street for buses going in the other direction. So the software at the bus stop would need to be able to identify and ignore data for buses going in the wrong direction.
I am assuming that the wireless device on the bus will send the data about the number of the bus and its destination.
To be honest I don't see much added value with your proposed system. It would be a lot easier to provide the information on a display beside the door of the bus and from a loudspeaker on the bus. That would also reduce the problems of vandals breaking the equipment at the bus stop. And not all bus stops have an electricity supply.
To my mind what would be a lot more useful would be a display at the bus stop that tells you how long until the next bus for each route arrives. I regularly use a bus that has a 1 hourly service in the evenings. It is a long route and it is not unusual for the bus to be 10 or even 20 minutes late. It would be reassuring to have a display that confirms that the bus is actually on its way and has not been cancelled. But that is not easy to implement and is probably not an Arduino project. And there is still the problem that the bus stop I use does not have electricity.
However, even for the purpose if providing live route information I suspect it would be more economical to provide the data on the bus company's website so I could access it with my smartphone.
...R