Today my wife and I headed to Dovški Križ from Vrata. I have to admit I was a bit scared because of all the parking fuss in Vrata, so we preferred to take the bus from Mojstrana. The timetable is posted on the Kranjska Gora municipality link.
https://kranjska-gora.si/novice/turisticni-avtobus-v-kranjski-gori The experience itself was very positive. Maybe just a comment, for the return we got on at the first stop at the end of Vrata and the bus was full, so it couldn't take anyone else on the whole route. On the tour we didn't meet a living soul. Don't know if it's because people are avoiding Vrata a bit, as 2 years ago bivouac 2 was full.
To describe the parking regime as the bus driver explained it to me. Before entering Vrata there's a barrier which isn't operational yet. Parking fee is collected only at the end of Vrata because only there is the machine, price 5€/h or 25€/full day. If parking somewhere by the road, it's still free, but be aware that parking is prohibited on unmarked spots on the entire Vrata route, so you're in violation. Today no fines were issued.
From mid-September a new regime is expected.