score:1
Looks like a taxi may be your only choice. Here is one for €120. Less should be possible if you can pair up with another or others, and asking in Portorož or Piran might turn up something a little cheaper. You would need to be departing around 08:30.
Upvote:3
This is old, but still can be useful for some people in the future. We have public transports, such as railway and buses, which you can check most at:
railways http://www.slo-zeleznice.si/en/
buses https://www.ap-ljubljana.si/en/
The third option is https://prevoz.org which is paralel to https://www.blablacar.com but it's used mostly for inside traffic through Slovenia, but its waaaaaay cheaper. You can get nearly anywhere from Ljubljana for 5€. For different cities to others the price may vary, but it's always between 3€ and 10€.