The online search takes into account all short term schedule modifications. Considering how many such changes occur on almost daily basis, you would be quickly complaining about data usage from all those schedule updates. Or you would frequently get wrong route.

Either way, a lot of complexity / resources spent on something trivially solved by the original solution (webpage).

Some buses don't have schedules, just an estimated frequency. Or some have schedules but don't stick to them with any reliability.

There should be paper schedules available in the station.

Then download the schedule from the web site?