#2: If the margin of "it could be early" is more than five minutes before it's supposed to come, you're sitting out in the cold for long enough to get cranky and frostbitten.
#3: If you happen to be almost early enough, you can't run for it because the sidewalks are covered with ice so even a slow walk is perilous
#4: If the bus in question runs less frequently than every 15 minutes, this escalates from being annoying to being a reason to go home and get back in bed.
If the city wants to encourage more people to take public transit, make it less of a trial. I know they can do it.