I agree with the posts above about staying in Pontresina instead of St. Moritz.
If you are taking the bus portion of the Bernina Express as well, you definitely want to start your journey in Pointresina instead of Chur—-that would make for a very long day.
Have you looked at the Bernina Espress timetable?
https://www.rhb.ch/en/panoramic-trains/bernina-express
There is only one bus a day in each direction. The bus to Lugano departs Tirano at 14:20. To make that bus, you need to be on the Bernina Express that departs Chur at 8:32, and stops at Pontresina at 10:22. You arrive at Tirano at 12:50 and have an hour and a half before the bus departs (lunchtime?). The bus doesn’t get to Lugano until 17:30. That would make for a VERY long day if you started in Chur.
When are you going? You need to make sure the bus is actually running on your day of travel. It begins running on weekends in March, but does not make daily runs until 28 April.