Also a long time back in 1986, my favourite experience was not exactly a delay of the flight I was booked on, but the happy outcome of an airline bus stuff up.
On a business class ticket on route from Stockholm to Washington, I had an overnight at LHR at BA expense.
BA advised me to be on a certain shuttle bus to T4 for a noon departure, and I was on that bus. We then stopped at another hotel where a group of people were waiting and duly loaded their luggage and got on. Then there was a long discussion (argument really) about whether this group were supposed to be on the bus, and they finally got off. As they recovered their luggage some zealous member of the party also took my bag.
Got to T4 to discover my bag was not on the bus.
As it was now only an hour to departure I went in to check in and find some help find my bag.
Sorry sir, we have given away your seat and the flight is full.
I said something, politely of course, along the lines ... I was staying at the airport at their expense, their bus collected me for the flight and was late, and to top it off they managed to lose my bag between the hotel and airport.
At this point a guy in a suit standing behind the counters came out to me and asked if I would mind waiting an extra hour for a later flight, to give them a chance to retrieve my bag, and that I would arrive in Washington before the original flight. He then took me to the Concorde check in.
My bag arrived by taxi a few minutes later, I checked in and had the Concorde lounge (direct boarding) to myself for a little while before other passengers arrived.
Flight time was 3 hrs 50 mins, and arrived Washington before we left London, and well before the B747 flight.
In those days you could visit the coughpit which I did while we were going at Mach 2.
So my airline bus delay resulted in arriving early.