Flights
You can fly into either of two airports near Milan:
Malpensa Airport is the big one.
Linate Airport is the smaller one. Just a touch farther away.
Car Transfers
Taxis are easily hailed at either airport and can take you directly to Bellagio.
You can alternately arrange car service with:
We recommend booking your return taxi to the airport several days in advance. Your hotel can easily arrange this for you, or you can book yourself online.
The Scenic Route
If you've got time to kill on the way in or out, and not for the heavily luggage burdened...
You can take a car to Como, and then the ferry between Como and Bellagio. On a sunny afternoon this is a beautiful way to see the southwest of the lake. Just make sure to get one of the fast ferries unless you feel like stopping at every town along the way.