Through Varenna is the best way. You've already been to Como, so you know that's not a town to visit. Taking a train there, then a bus or ferry to Bellagio is the long and hard way to do it.

I assume you'll be at the Milano Centrale train station. From there, purchase a ticket to Varenna-Esino. It's a one hour and three minute ride, and costs E6.5. Walk a block or so downhill to the lakefront where there is a ferry stop. There are frequent ferries that connect to almost every town on the lake. From Varenna it's one 5 minute ferry ride to Bellagio.

One hour train to Varenna, 5 minute ferry ride to Bellagio is the fast, easy, scenic, cheapest way.

Using the Trenitalia website for this is tricky because it is a regional train. Here's a sample train itinerary:

https://www.lefrecce.it/B2CWeb/searc...D=RPy4satTneOg

When you do a search make sure you click "tutti il treni" because searching normally just brings up the national trains. Also, you have to put in Varenna-Esino, not just Varenna. Also, since it's a regional train it only shows the train schedule to five days in advance. You can't search now for a train in August. Finally, since it's a regional train you don't need reservations. There is no discount, and no need to pre-purchase. You can buy the ticket when you get to Milano Centrale if you want, or buy it online within five days of using it.

Bellagio is beautiful, but commercial. Varenna is small, but more untouched, and worth a stroll.