According to this link Milan-Bergamo is currently one of the three airports where luggage can be checked through. The implied constraint seems to be that the journey is booked as a connecting flight, there's no information about being able to do this if you book the flights separately.
However, it seems that this particular route can't be booked as a connecting flight at the moment - there's a list of some of the flights that can be booked as connections here. They can be booked in exactly the same way as a single flight through the Ryanair website.
Checked baggage fees will be charged per sector of each journey.
Ryanair will be able to transfer your baggage to your final
destination at Fiumicino, Milan Bergamo and Porto airports only. In
the event of disruptions leading to your flight being diverted to
another airport, or where you are being re-routed via a different
airport, Ryanair will be unable to transfer your baggage. As a result,
you will need to collect your baggage at the intermediate airport and
re-check-in at the check-in desk.
In summary, this seems to mean you'll have to book two separate tickets, and collect your luggage at Milan on this itinerary.