Italy to Slovenia by train

There is really no direct rail link between Italy and Slovenia, odd as that seems. The closest is to cross the border by bus or taxi at the Italian town of Gorizia to the train station at Nova Gorica in Slovenia, just over the border. Fastest way is by bus, I believe from Venice Marco Polo Airport.
You can also go by way of Villach, Austria.

Train schedules will reflect most departures going via Villach and fewer via Gorizia. Local buses and taxis run across the border from Trieste, if you're just trying to get a short distance, like to Koper. For longer bus connections from Venice, see DRD bus (1 or 2 daily) and GoOpti shuttle service. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.

We would like to visit Ljubljana and Lake Bled.

Depending on where you are coming from in Italy, you might check GoOpti transfer service ( http://www.goopti.com/en/). Based on reviews and costs, I considered using them during a trip next month, but I decided to rent a car in Italy since I'll be doing a bit of driving around Slovenia before returning to Venice.