When I was a kid, the "school run" simply didn't exist.
If you lived more than 3 miles from the school, you got a free bus. If less than 3 miles, you were expected to walk or cycle (I used to cycle, it was about 2.5 miles to my grammar school after the first two years, before that it was bus.).
It really should not be necessary now. One day last year, I happened to be cycling through Cowbridge when the local comp was finishing, and I counted 14 school buses between the traffic lights and the school, so why does any parent need to drive their kids to school?