>> It appears that Lugano to Tirano is a bus journey
Yes. It operates only once per day, leaving Lugano at 10:00, arriving Tirano at 13:00.
>> and onward journey to St.Moritz to Davos to Chur is a train journey.Right?
Yes, it is a train, but the route is not Tirano - St. Moritz - Davos - Chur.
The direct Bernina Express goes from Tirano to either
Chur (once per day) or
St Moritz (twice per day) or
Davos (once per day)
If you get the Bernina Express to St. Moritz or Davos, and you want to go to Chur, you will need to continue your trip on regional trains. Regional trains don't have panoramic windows, and don't require reservations.
Taking the Bernina Express bus from Lugano gets you to Tirano at 13:00:
> To get the Bernina Express direct from Tirano to Chur, you will need to wait until 14:26.
> If you prefer to leave earlier, you could take the 14:03 Bernina Express to St Moritz, and continue to Chur on regional trains. To get this option, put "via St. Moritz" into your timetable search for the trip from Tirano to Chur. The route from St Moritz to Chur on regional trains is essentially the same route as the Bernina Express follows.
> If you want the fastest trip from Tirano to Chur after arriving at 13:00, you will need to use regional trains. There is a regional train leaving at 13:40, and you would change trains at Pontresina and Samedan on your way to Chur.
If you want to get back to Lugano the same day, use the timetable to find connections "from Lugano" "to Lugano" "via Tirano" and "via Chur". If you don't want to pay extra, avoid the routes through Monza, where your Swiss Travel Pass is not valid (because it is in Italy).
Bernina Express trains are shown in the timetable by the letters "BEX".