Navigating on public transport inherently requires full data on public transport timetables.
Public transport timetables are out of scope of OSM, there is no good way to enter them, they raise copyright concerns, they would quickly be outdated. So OSM is just the wrong tool for the job…
I use an app called "Öffi" https://f-droid.org/packages/de.schildbach.oeffi for calculating routes on public transport. It queries the open APIs of public transport networks. I don't know whether it supports the one you need, but e.g. in Germany and Austria it is very usable.
