I had a weird issue with DST. I was on an overnight bus going home, and trying to sleep although the driver had to wake up passengers to call out stops. But at a certain point he just parked for an hour and explained that he needed to do that because he needed to stick to the schedule, which was based on the prevailing time.
I have heard of some interesting issues with trains. Amtrak generally waits at a station or at a siding when DST is over in order to maintain the schedule. For DST going into effect, apparently they try to make up the time as best they can, since they're typically slack built into most train schedules. I've been on a train where they literally slowed down to a crawl since they would otherwise be well ahead of schedule. It gets really weird in areas without daylight savings time.
For that bus, the procedure is likely to use up as much slack as possible and then to minimize waiting times. But they'll probably still be late relative to the timetable. However, arriving late is better than leaving early, which tends to strand passengers.