Transportation

Bus, I suspect. Might be two separate buses, one to Ljubljana and another one to Bled.

Whether you have bags, and your destination after Bled, might affect that but you haven't
noted that info here. Also what your definition of "best" means (I assumed cost-effective,
but if you want a private driver, I think others can help with that).

Train from Zagreb to Ljubljana taking 2:15. Then take a bus from bus station adjacent to Ljubljana’s train station. Buses take from 1:05 to reach Bled.

For a reliable option use the bus. For a more confortable option (but costlier) book a private transfer. This can be good if you want door-to-door service without having to worry about bus schedules. Ivan Ćosić (MC-Travel Croatia) does those so it's good to see if it's worth it!

If you want to compare prices, check the cost on Daytrip.com; about 200 euro. But what I like about them is they will make stops and make recommendations on where to stop. Sometimes is worth visiting the site just to see the list of possibilities between two points. With a couple of stops figure 270euro for that trip.

Take the bus from Zagreb, you’ll likely have to change busses and operators/lines in Ljubljana. Busses from Ljubljana to Bled are pretty regular, every few hours at most. Check Flixbus for the intercity leg schedules.

Yes, there’s a train between Zagreb and Ljubljana, but I’d still pick bus. I took the train and it was miserably hot and packed in July. And I think it took longer.

Thank you for the ideas and information.

Have a great trip!