No. He got out at the next bus stop.
Note that "airport" is one word, not two.
In my opinion, "caught" doesn't work with taxis. In BrE, we "get a taxi". You can also take a taxi or, if you call for one by telephone to come to pick you up, you book a taxi or call a taxi. The use of the word "cab" is very common in the UK too, as well as "taxi".
Student or Learner