jQuery Forum

If you locate some web service that can provide the schedule and routing data, you can use jQuery $.ajax() to send the required data to the server.

However, you state it needs to work offline, so you will have to create either a webapp (you need to create a manifest file) or hybrid app (use PhoneGap, etc.) You'll need to see if the transit agency can provide you with data and regular updates to populate a local database. And you'll need to find some library for doing the routing that will be practical to run on a mobile device. (This is usually done on a server.)

All of this is well beyond the scope of this forum. We can help you with jQuery Mobile problems as they come up.

Good luck!