To be honest, this sounds more like an electronics project. I'm assuming that the GPS signals (if they even exist) are not publicly available, and probably scrambled (encrypted). This means, it would be illegal for you to try and access them.
I have considered the possibility that it isn't public, but I wanted to gather some information before going to the public transport office, to avoid saying "I wanted to ask you if you are interested in this app, even though I have no idea how to make it".
My idea was to understand how it works, try it with some friend's smartphone and then consider the market possibilities.
The biggest problem would be communication between GPS module in a bus and some kind of server. Most GPS trackers use GSM module to do so. Host send command through SMS and then receive coordinates back.
How to place coordinates on map (like google map) you can read online (there is lots of resources about such).
Let me see if I got it right: a GPS receiver gets data from satellites and calculates the position. A server somehow connects to the receiver and asks for the position, and can then serve that information to anyone who wants them, correct?