You can easily get to Stara Moravica in 3 1/2 hours by train from Budapest, Hungary, or from Belgrade, Serbia, on a 3 hour train ride. Get off the train in Subotica and take a 30 minute cab ride or get off in Backa Topla and Stara Moravica is about a 15 minute cab ride.
You can also arrive by car using the M5 from Budapest or E75 from Belgrade. If you are coming from Budapest, the trip requires an international border crossing that will add time to your trip. This crossing can add up to about 1 hour.