Since you are supposed to land in Milan, you can take the “Volpi” coach that leaves for Genoa from Terminal 1 – Arrivals floor – Exit 4 – Stop 17. The ticket can be bought on board.
You should get off the bus at the Principe railway station stop in Genoa. In case, you can ask the driver to show you where the stop “stazione Principe” is.
If you are late for getting the bus to Genoa, you can get the bus “Malpensa Shuttle” which leaves from Terminal 1, Arrivals floor – exit n. 5, stop n. 4 every 20 minutes, and get off the bus at the stop “Milano Centrale” (Milan Central Railway Station). You can buy the ticket on board. When you get to the Station you can reach Genoa by train (the stop is “Genova Piazza Principe”).
How to reach Genoa from the airport “Orio al Serio” in Bergamo:
If you arrive at Orio al Serio airport (Bergamo – BGY) you can take the shuttle bus to go to Milan. There are several bus companies that can bring you to Milan railway station (Milano Centrale) and the fares are the same: 5 or 6 € one way. In some cases, if you can buy the ticket online in advance or if you buy the round trip, there are some discounts. Here the websites of the two bus companies:
How to reach the railway station “Principe” from the airport “Cristoforo Colombo” of Genoa:
There is an efficient shuttle bus airport to Principe train station available every day from 05:20 am to 11:30 pm. The service is called “Volabus” and there is a ride approximately every 30 minutes. The ticket costs 6 Euros and you can buy it directly on board the bus. You have to get off at the “Genova Principe railway station” stop. For more info please visit AMT website.