My primary school was only half a mile from home, so I walked there (on my own, obvs.), except when the week of Cycling Proficiency came along, and everyone in my year cycled there, parking their bikes in the (long) drive by just leaning them, unlocked, against the hedge. The day I passed I went for a ride with my Dad "round the block", then "round the block but using the next road over" then "round the block using the next road over after that."
I left that school to go to grammar school six or seven miles away and went by train and bus (free season ticket and bus pass), although I did go through a phase of cycling across town and parking my bike at some friends of my parents who lived a stone's throw from the station. I doubt it saved me any time though. Occasionally in the sixth form I'd cycle the whole way. The class room must have been minging, full of the smell of teenaged boy. I remember when I was in the third or fourth year, our English teacher, Paddy Carpmael, asked who would like to go on a bike ride at half term. I was up for that, as were a handful of others so we turned up with bikes. I don't remember any permission forms or mass of paperwork, just bikes and a pack of sandwiches. We went up Leith Hill, and Mr. Carpmael bought us all a half of cider in Coldharbour.
I was (and still am) in Scouts, and we'd organise ourselves to go off on a bike ride on Sundays. No leaders, just half a dozen hoodlums on bikes, more sandwiches, no helmets (they hadn't been invented), minimal (if any) tools. We had to knock on a door to borrow a spanner as one kid's rear wheel had shifted in the dropout and was fouling the nearside chainstay.