New Line Bratislava – Istria
As of today it is possible to travel with direct line from Bratislava to Vienna, Zagreb and the most popular towns in Istria. The line which is operated by Crnja Tours from Rovinj, runs everyday year around, except for on some public holidays.
The departure time from Bratislava is 03:45 AM so you will have to get up early to catch the bus. Departure location is the main bus station at Mlynské nivy, 821 09 Bratislava, which is a fairly big bus station, so make sure to get there 15 minutes before departure so you have enough time to located the bus, which departure from Peron 15.
The travel route from Bratislava is the following Vienna, Graz, Zagreb, Rijeka, Pula, Porec, Rovinj, Novigrad and Umag the travel time between, Bratislava and Zagreb is 6 hours and to the end station in Umag 12 hours and 30 minutes.
Obviously there is also a daily bus travelling from Umag direction Bratislava, that bus departure from Umag at 10:15 and arrives in Bratislava at 23:00 (11 PM). You can see more info about the bus from Umag to Bratislava here.
If you are travelling to other destinations in Croatia, you will have to change bus at the main bus station in Zagreb, for some destinations like e.g. Split and Zadar you can buy a ticket from Bratislava, which include the bus change in Zagreb.