This is the most wonderful of places. On the very tip of a peninsula on Lake Como, it actually seems like an island when you visit. The best way to go to Bellagio is to catch a ferry at Varenna, also a nice town to visit in its own right.
There is a ferry timetable in the house. In summer the services run frequently, there’s such a short time between services that a relaxing “Campari” at a local bar will see you through to the ferry arriving. Avoid going to Bellagio on a Sunday or Monday public holiday for obvious reasons. Maybe you could telephone for ferry service hours and ask which day or half day shops shut in Bellagio. Remember not to miss the last ferry!
Bellagio can be a bit disappointing with the locals as they get a lot of tourists there, might I suggest if it’s a beautiful day you have a picnic. Just buy your rolls, cold meats, cheeses a bottle of vino at one of the local supermarkets. Buon Appetito.