Susan and Nicolas have made good suggestions, I have two more comments.

You wrote... I went to the bog. I don't know what a bog is.

You wrote... I had to get back to the toilet.

This should be... I had to go back to the toilet. 

Trip To The Airport

On the road to the airport my bus ran over a man. The bus driver got off from the bus and and called the ambulance. Luckily there was a tube stop and I could get a train. At the airport I had to stay in queue for at least 30 minutes (half an hour). Getting into the duty-free zone, I bought cigarettes to take abroad and then I went to the bog. The gate opened and I waited in line for my turn, but when my turn came I couldn't find my ticket and I had to go back to the toilet to look for it. The ticket was on a shelf over a wash basin (or sink). In the end, and after two calls, I succeeded in taking the airplane(boarding the flight might sound more natural here).

Trip To The Airport

On the road to the airport my bus ran over a man. The bus driver got off from the bus and and called the ambulance. Luckily there was a tube stop and I could get a train. At the airport I had to stay in  a queue for at least 30 minutes (half an hour). Getting into the duty-free zone I bought cigarettes to take abroad and then I went to the bog. The gate opened and I waited in line for my turn, but when my turn came I didn't find my ticket and I had to get back to the toilet looking for it. The ticket was on a shelf over a wash bowle. At In the end, and after two calls, I succeeded in taking the airplane.