Passanger AI has a formula which decides, by which means they travel to other locations.
Waiting time, so frequency is a huge factor in it.
I guess, the frequency for your intercity-busses is higher than the frequency of your trains.
So people tend to use your busses because they don’t need to wait that long for it.
Also I think, the travelling time to your train station might be too high and/or the traveltime to the other city might be too high, even with trains.
When you remove the Intercity busses, the travel time+waiting time seems to exceed the 20 minute limit, if it takes for the AI more than 20 minutes to travel to an other location, they won’t travel there.
But without Screenshots or a savegame-file so everyone could look for himself, the cause can’t be determined for sure.