You can take the Swiss postbus (postauto) system's Palm Express from Lugano in the Ticino to St. Moritz. The 3¾-hour trip passes through a corner of Italy and over the Maloja Pass. The bus runs twice daily from mid-June through mid-October; reservations are essential. Owners of a Swiss Pass will need to purchase the additional Alpine Ticket for 15 SF.
Palm Express (081/8376764 or 091/8078520. www.swisspost.com). Note that the timetable and itinerary search is the same as Swiss Railways, so you will receive schedules for both bus and trains.