From Zagreb to Umag, there are direct bus all year around, depending on travel route there is a distance of 260 to 285 km between the two cities, the most common route is via Rijeka, but some routes also go via Trieste in Italy, travel time by bus is about 5 hours. Bus timetable from Zagreb to Umag you can see below, and departure time for buses from Umag to Zagreb you can see here.
If you are travelling from the airport in Zagreb you first have to go to the main bus station in Zagreb. If none of the schedules below should match your travel plan, you could try travelling Zagreb to Rijeka, and then continue from there on to Umag.