Our process was this: as soon as we saw our bus, I removed my DD from the umbrella stroller and DH folded it up. Then we all boarded the bus. One of the occasions that we held others up a bit, we were in the front of the line, the bus came around from behind another bus, he started to fold it, but realized there was something in it, a folder of pictures, and it took him a bit to get that out and put it in a backpack. We had not been keeping things in the pouch in the back of the stroller and another adult with us had put it there, so it was just unexpected. I made it to the bus with the kids, he was still at the line just finishing up, and the people behind him were annoyed. It was approximately 30 seconds between the bus arriving and the stroller being folded.
The second time, we followed the same process, but the clasp on the side of the stroller that holds it closed broke, the stroller popped open, and he reached for the clasp, and then had to fold the stroller back up and get it to stay closed. Again, the kids and I ended up about 3 yards ahead of him.
These situations make me very tense, especially because the first time, the couple behind us got huffy about it, so I am very self-conscious regarding the time, and know both situations were way less than a minute.
I agree with you that it is reasonable to start the process when the bus approaches. With an umbrella stroller without items stored in it, it's more than enough time. But things happen. And there seems to be the assumption on this thread that things happening just means we should break the stroller down way earlier to make sure that even if things happen, nobody is inconvenienced at all.