how to travel from bulgaria to italy by train?

From Sofia you get a train to Belgrade and from Belgrade you go to Zagreb and then to Split. From Split or Dubrovnik you can then get the ferry to Italy.

The connection runs once daily, leaving Sofia at 20:50 hrs and arriving in Split at 20:48 the next day.

You need to check whether there is a ferry matching your arrival.

http://www.cemar.it/dest/ferries_croatia.htm

An alternative route is going via Greece and catching a ferry via Greece.

Or going from Sofia to Belgrade, from Belgrade to Ljubljana and from Ljubljana to Venice. Best look for yourself at http://www.bahn.de

If you are close to the Romanian border, you can also consider taking the bus to Italy. Lots of Romanians work as seasonal migrant workers in Italy, many Italian cities have very cheap buses to Romania.