List of bus stops from Google Maps

The Google Places API does have stop information on there but you need to form your query very specifically to make it work.

The key is using the nearby search with rankby=distance and radius= and types=bus_station

The default rankby prominence rarely shows bus stations.

Sample query:

https://maps.googleapis.com/maps/api/place/nearbysearch/json?location=49.89458,-97.14137&sensor=true&key=your_key&rankby=distance&types=bus_station

This is not a service that Google provides. They surely have all of the stuff you need on record, but they do all of their calculations internally.

One option (which might be a bit difficult) is to mine public transportation schedules for their bus stop locations. It might be an option if you have a small region (ie. a city) that your web app is to support. It's risky because if the pages change then you'll have to reconfigure the data mining application, but you'd still have the same problem trying to mine the data from Google (or somewhere else) - if you could find a way to get a bus stop list with locations and built your app around it, it could change at any time and break your application.