Go to the link below. That is the company running the buses.
Scroll down to Linee Extraurbane (Extra Urban Lines). The line you want is C112.
Click on Orario Invernale (winter schedule) which is effective after 12 Sept 2025 until June (basically during the school year). Remember that dates outside the US have a DD/MM/YYYY format, so don’t get confused.
To see the schedule from Menaggio to Lugano see ANDATA (going). From Lugano to Menaggio see RITORNO (return)
Above each bus number column there is the type of service note, which indicates the frequency. Since these buses are primarily operated for workers and students try to travel on weekdays as the buses will be more frequent. Remember that in Italy kids go to school Monday-Saturday, and Saturday is often a working day, at least in the morning. FERIALE in Italian means working day, from Monday to Saturday. These are the notes:
SCO5 Mon to Friday on schooldays
0006 Saturday only (but not on a Saturday that is also holiday)
006 Saturday school day only (therefore would not be operating during the Christmas holidays)
FER5 Monday to Friday
FER6 Monday to Saturday
GIO3 Daily (“Giornaliero”), therefore Monday to Sunday, excl Christmas Day and New Year’s Day.
SCOL School days from Monday to Saturday
FES3 Sundays and Holidays (“Festivo”) except 25 Dec. and Jan 1.
https://www.asfautolinee.it/orari-in-pdf/
I think you can pay for the ticket on board with credit card or phone on the tap and go device on board. You might need one separate credit card per passenger (in other words I don’t think you can pay for two passengers in the same card) Read below. In any case go to the Lugano stop (at the main train station) a few days ahead and inquire with the driver.
https://www.asfautolinee.it/swipe-on-lake/?lang=en