Given that you'll pay specialty baggage fees to transport your own bike to and from Italy, the hassle and expense of buying a bike suitcase or box, and storing it, you might be better off renting a bicycle while you are there, if your trip is less than two weeks long and you are flying from the USA. If, however, you are flying within the EU or your trip is longer, it might be cheaper to bring your bike.
Example 1: Flying from USA
From the USA, the fees would be US$300 ($150 each way) if you flew on Delta to Italy:
Bicycle Transport Fees
150 USD/CAD for travel to all regions (excluding Brazil, Europe, and North Africa)
150 USD, 175 CAD*, or 125 EUR* for travel to/from Europe or North Africa
75 USD for travel to/from Brazil
*CAD amount will be charged exit Canada, and EUR amount will be charged exit Europe.
Example 2: Flying within the EU
The original-OP was located in Ireland, and for Aer Lingus within Europe the fee is not so bad. 80 euro total (40 each way) if you declare ahead of time:
For all other Aer Lingus flights, Sports Equipment is subject to a fee of €40 or equivalent payable online prior to departure; or a fee of €50 or equivalent payable through our reservations centre or at the airport on the day of departure. This fee is charged per passenger, per direction.
However, many European carriers do not charge any fee at all for bicycles.
Conclusion: Flying Versus Renting
If this vendor that rents bikes in Italy is any guide, it'd cost about 300 euros to rent a road bike for twos week in Italy. So for an American, the break-even point with the airplane fees (around US$300) is two weeks.
For Europeans, it'll almost always be cheaper for the EU-rider to bring their own bike.