Important point: The Bernina Express doesn't run from Lugano. It runs from Tirano to Chur. Details here: https://www.rhb.ch/en/panoramic-trains/bernina-express
There is a once-per-day BUS which runs from Lugano to Tirano, to connect with the Bernina Express.
Timetable here: https://www.fahrplanfelder.ch/fileadmin/fap_pdf_fields/2020/90.731.pdf
Depart Lugano (station forecourt) 10:00, arrive Lugano 13:00.
Bernina Express depart Tirano 14:25, arrive Chur 18:19
There are lots more trains Tirano to Chur, but only one bus.
As regards Lugano. I would spend half my time in Lugano town, just exploring and walking along the lakefront. I would spend the other half taking a boat trip on the lake. Make sure the boat trip includes stopping at Morcote. Why Morcote?, click here for photo or google for more.
Hotel: Lugano town centre is on lake level, the station is up a hill behind the centre. The two are connected by a funicular. Any hotel in the town centre near the bottom of the funicular would be good.