There is a regular train on this route every hour (there is a regular train on every Swiss rail route every hour!). The named Bernina Express is an extra train and is the only train that needs reservations. You see the same mountains through the windows of all the trains.
So yes, you can go to any station along the route (and any station in Switzerland), and there will be a train in either direction within 60 minutes, no reservations needed.
You can look up train times on the Swiss Railways website: https://www.sbb.ch/en
The Bernina Route runs from Chur - via and lots of other places to Tirano.
The Bernina Express doesn't actually go via St Moritz, it goes via nearby Pontresina, so if you are going to or from St Moritz you will need to get a normal train for at least part of your route.
From Tirano you can get a train to Milan (only once every 2 hours, it is an Italian train so Swiss rules don't apply).
Or you can get a bus to Lugano. this is a bus and only runs once per day:
Tirano, Stazione, depart 14:20
Lugano, Stazione, arrive 17:30