Looks like you’ll have to take the train from Verona to Bled.  The absolute fastest I see is almost 6.5 hours.  Overnight trains take longer, but you wouldn’t be using up time in the middle of the day.  CHeck timetables here:
rotocol=http:&” title=“http://reiseauskunft.bahn.de/bin/query.exe/en?newrequest=yes&amprotocol=http:&”>http://reiseauskunft…
 
Where in Croatia to Rome?  A flight will be your fastest option: http://www.whichbudg…

Flying is fastest, but if you can’t find a cheap flight from Croatia to Rome, then look at overnight ferry plus train — it’s not a bad deal.  You can ferry from Split to Anacona then catch a high speed train to Rome.  You can leave about 7 PM and be in Rome the next afternoon, so you really haven’t lost much time over a daytime flight when you consider time to get to and from the airports.  You can also ferry from Dubrovnik — I think to Bari and catch the train to Rome.

Train from Verona to Bled in 6.5 hours is fine. I looked at the link you sent with the timetable. It doesn’t display prices. Where can I find prices? Must I order tickets in advance?
 
At the end of my trip I need to get from Croatia (anywhere along the coast, preferably not far south) to Rome. Can I trust the flights to be on time? I must catch from Rome another flight, a little before noon, so I must be there on time.

Can you please tell me where I can find exact timetables and prices for the ferry from Dubrovnik to Bari and for the train to Rome?

Try http://www.visit-cro… for basic information about ferries and links to the various ferry companies where you can get schedule and cost information. 
Jadrolinija is the biggest ferry company.

take care your self.
http://travelbackpac…

Take the train.