From Zagreb Airport to Slovenia
There is a bus every 30 minutes from Zagreb airport to the main bus station (the timetable can be found HERE). The bus trip takes approximately 25 minutes. Every monday and friday  at 11.30 a bus departs for Slovenia which goes through Novo mesto then continues to Ljubljana.
For travel by train, take tram no. 2 or 6 – click HERE for the timetable - to the main railway station from where there are several daily railway connections with Slovenia available, which you can find HERE.

From Pula Airport to Slovenia
From the airport you can go to the main bus or railway station by taxi, or transfer, which has to be ordered in advance. 
There is a bus to the Slovenian coast which departs every morning at 5.30 from the main bus station, and the train to Ljubljana leaves every day at 18:15 from the main railway station, the details can be found HERE.
Transport services from Zagreb and Pula airports to Slovenia are also offered by the low-cost carrierGoOpti.