Is it doable to get to villa carlotta from bergamo by public transport ?
Yes, one way is get to Milan Central by train or bus, then train to Varenna, then a ferry to the nearby villa
Not aware of any bus line or train that goes directly from Bergamo to the villa stop, maybe there is.
Another possibility is bus C46 from Bergamo to Como then bus C10 to Tremezzo.
asfautolinee.it/content/it/orari-rete-extrau… (only in Italian )