Car not essential, but advised above all to go Milan or Como or Lecco.
If you come without car, you can come through Como San Giovanni Station, take the bus from there to Bellagio; alternatively you come from Milan untill Varenna, and cross the lake by ferry; Varenna station is up, if you have some luggages take it into consideration.
If you have got a car the way from Lecco is a little bit shorter, with less curves.
From Milan you take the Superstrada SS 36, you exit at Valmadrera ( just before Lecco ), you cross the town, and then left at the lake border till Bellagio.