Bus Service from Tirano, Italy to Lugano, Switzerland

There is only one bus per day and it is by reservation only, part of the Bernina Express. Right now, I am finding no reservations available in the month of December. Time for plan B.
https://www.rhb.ch/en/panoramic-journeys/bernina-express/

Plan B1 is a fun adventure across the lake - if it isn't pouring rain.
You can take the train from Tirano to Varenna-Esino, walk 1/4 mile to the ferry pier, and take the ferry to Menaggio, which is fairly frequent (hourly or better). From the Menaggio pier, it is a slightly longer walk to the Via Lusardi bus stop (southbound) where you take can take bus C112 every 1-2 hours, but only until 5.30 PM or so.

About ~3.5-4 hours if all goes well, but wait times might be long.

Plan B2 is easier and also takes about 4 hours: train from Tirano to Monza, where you transfer to a train to Lugano.

No reservation needed for either plan.

The Bernina Express bus to Lugano does not operate in December (and Also not in January). That is why you cannot reserve any seats on it...

So you need another option... Train via Monza is probably easiest.

There is a bus called the Palm Express from St Moritz to Lugano, but it travels over the Maloja Pass, not the Bernina Pass. Right now, the cheapest ticket is with a Saver Day Pass, otherwise it is 92 CHF without a Half Fare Card.
At sbb.ch, it contains this note in German, which I translated with Google Translate.

Palmexpress: Mandatory reservation (free) via SBB Mobile or sbb.ch up to 1 hour before departure. To reserve, click on "Tickets from" and then select whether you want to reserve with or without purchasing a ticket. For information, call +41 848 818 818

Since I imagine you wish to travel over the Bernina Pass by train, the route through Monza works.