Bologna to Perugia by train

Trenitlalia is the national rail operator in Italy and in addition to its cheaper types of ticket; it also typically offers other discounts available to non-Italians, which include:

• Group Offers, provides for a discount of up to 50% when 3-5 Adults travel together.
• Family Offer for when groups of 2 - 5 people are travelling together and at least one of the party is a aged 11 and under.
• The Children Free Offer is available for journeys by Frecce trains, when groups of 2 - 5 people are travelling together and at least one of the party is a aged 15 and under.
  Those aged 15 and under travel for free, but the Adults will need to purchase full price 'Base' tickets.

Italiarail lives up to its name by selling tickets for rail journeys within Italy and the core feature of its service is that it is primarily designed to be used by international visitors to Italy.
So the English translations of place names are used when looking up journeys and the terms and conditions for using each type of ticket are clearly explained.
It also clearly points out the additional costs of upgrading to other classes and types of tickets while spelling out the additional benefits of doing so.
Though Italiarail will charge a booking fee, typically of around €3.

The Early Bird service

Italiarail has launched an 'early bird' pre-booking service for journeys by Frecce trains.
Tickets can be booked up to a year ahead of travel at a flat-rate price per route, before the tickets have been released for sale by Trenitalia.
If when they are placed on sale, the price is cheaper than what you have already paid to Italiarail, it will automatically refund the price difference.
Conversely, if the price is more expensive, you won't be charged the price difference.
You can also have the peace of mind of securing your seat(s) on the Frecce train(s) when you are first planning a trip.
If before the tickets are placed on sale, you decide to change your plans, you can request a refund; but once the tickets are released for sale, you will then be bound by the terms and conditions of the ticket(s) you have booked.