May 3, 2016 - 7:30 AM
You should at least pre purchase the seat reservations if you want to travel on the actual Bernina Express, rather than one of the local trains. Please see here.
But before you buy any tickets I'd recommend to first list all of your travel plans and see whether a rail pass is an option for you. In that case the Bernina Express would be included or discounted. Rail passes are explained here, and how to pick one is explained here.