the past 2 busses i have caught have been insanely last minute. i Just bought a ticket after my bus was scheduled to leave & caught it 4 minutes after scheduled departure.
The other time, I was walking around with 3 minutes to spare in the wrong direction in manhattan, realized, ran, and found the gate underground.
I have done the same with flights, catching it running on as the last person boarding the plane.
Needless to say, yes i've missed a lot of busses in my time as a chronically late person, but also, it has given me a deep faith in the world working out.