The Bernina Express runs from Chur to Tirano. From St. Moritz, you can take the direct local train which does not require reservations. You can just board if you have a rail pass such as the Swiss Travel Pass. If you don't have a pass, you need to buy a point to point ticket.
The bus from Tirano to Lugano can be booked through the link under "More on other websites" here. Booking is not open yet as far as I can see. The bus schedule of 2015 starts on March 28.
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