What is the best way to get from Ljubljana to Rovinj in late September or early October?
That depends. On lots of things.
Personally, I think the best way is by private helicopter (especially if someone else is paying). But that may not be ideal for everyone.
"Best" is pretty subjective. To get a more meaningful answer, you'll need to provide a bit more context about your trip and plans. Are you in a hurry? On a tight budget? Where else are you going and how do you plan to get around once you get there? How are you getting to Ljubljana? How are you planning to move on from Rovinj once you're there. Etc.
My husband and I rented a car and drove between the two cities in 2010. Our only difficulty was that Google maps routed us to an obscure border crossing only used by locals. The border guards wouldn’t let us through and we had to go to a larger crossing about 15 mins away. I wouldn’t hesitate to drive it again - I would just look a bit more closely at my map. Good luck!
Public bus (once a day in the morning?). Or GoOpti transfer perhaps - makes more sense if you have more than one in your party.
If you are picking up a rental car in Croatia, as I did on my last trip, consider what I did: I took the direct train (2X a day) from Ljubljana to Rjieka, picked up a car near the train station, and drove about an hour to Rovinj for a few nights. But I like trains and dislike long bus rides - maybe to you it doesn't matter. The train ride to Rijeka is nice although not quite spectacular.
Trains from Ljubljana to Pula take 5-6 hours with 2 connections, 2x/day. That's at least a back-up plan. You'll find buses to be more direct or frequent. Try www.rome2rio.com and "drill down" to follow links to the actual bus operators. You may not find actual September schedules before May or June, in some cases, but if they have service this spring, it should be similar in the fall. Expect minimal service on Sundays. Rick's Slovenia/Croatia transport summaries (guidebook pages 124 & 588) also suggest http://www.autobusni-kolodvor.com.
There are a few direct buses between Ljubljana and Rovinj in the summer months, but I don’t know how many of these services remain by late September or October. Flixbus has two daily Ljubljana-Rovinj buses in their timetables until October 1.
Another alternative is taking a bus from Ljubljana to Trieste (90 minutes) and changing to a bus to Rovinj there (2 hours). Check www.ap-ljubljana.si for the first leg and www.autostazionetrieste.it/en-us/linee/internazionali for the second leg.