One thing to keep in mind when renting a car is that the roads are very narrow and parking spaces very small, so you will want to think like an Italian when choosing the vehicle size! We made the rookie mistake of choosing an Audi Q2 (small SUV) our first time and it made things quite difficult.
I also recommend that you arrange parking for your vehicle while in Bellagio ahead of time, as the public parking lots can get quite full. The owner of our B&B had a small garage for us to use on the edge of town the first year but the second year it wasn’t available so, instead, he parked his own car in a space in the free public parking lot to save the space for us until we arrived which was super helpful!
If you don’t rent a car, Bellagio is still relatively easy to get to by public transport. If you are coming from the airport, take the train to Milan Central and then transfer to a train going to Varenna. Once in Varenna, you can take the ferry directly to Bellagio.
Alternatively, if you want a private transfer, the cheapest option I found is at https://airportstaxitransfers.com where a one way trip from MXP to Bellagio for up to 3 passengers is 115 Euro.