Long way round means to take a longer route to your destination than taking the direct route. It doesn't necessarily mean a ticket. Another way to say long way round is scenic route; taking the longer route instead of a direct route. You will hear scenic route in American English than you will hear long way round.
Ex: Let's take the long way round. I'm in no hurry.
Ex: I'm taking the long way round to Colorado. I want to take my time.
Thank you so much for your question!