9 years ago I also flew from Gran Canaria to Paris with a stop -over at Madrid. Our flight was delayed and we were killing time by walking around. From this moment in time, the experience takes an opposite direction from yours. Suddenly the delay was over and the final call was announced. We ran over to the gate where the shuttle bus had already left. However, they arranged for a minivan with a dedicated grim-looking driver to take us to the plane. I got in with my 3 months old baby girl. Before I completely closed the door, the driver sped away with smoking tires and screaming motor. I somehow figured it might be intelligent to put the saffety belt but held my baby in one hand and the other gripped the chair in front of me to prevent from rolling over. We took a 90° turn with 65 km an hour, cut in front of moving aircrafts and raced over the tarmac. My baby cried with laughter over so much fun while I was completely focussed on surviving. Ieeeepppppp , what a relieve we crashed to a stop at the stairs to the plane.
The intention of the service (taking us in time to the aircraft) was perfect. The way in which it was performed a bit over the top, in my view.