The once daily Lugano-Tirano bus is marketed as part of the Bernina Express route, but it is a bus. They don't sell tickets to/from Menaggio, so I stopped thinking (years ago) that you could board the bus there.
From Menaggio to Tirano, another option is to take the boat across Lake Como to Varenna, then walk the paved road directly uphill to Varenna-Esino station to catch a regional train from Varenna to Tirano; those train schedules are reflected at www.SBB.ch.
This spring, we heard that Varenna's travel agency (Viaggi del Tivano, sells train tickets) had moved from their old location on the main road by Hotel/Albergo Baretta to the south side of the train station itself (no ticket booth in the station). The regional train tickets are also sold at other Italian stations or sold at www.trenitalia.com within 7 days of travel.