I never did get my frequent flyer miles, by the way. I never do. I couldn't find the card in time. This has become a real frustration for me. Everyone I know — everyone — is forever flying off to Bali first class with their air miles. I never get to collect anything. I must fly 100,000 miles a year, yet I have accumulated only about 212 air miles divided between twenty-three airlines.
     This is because either I forget to ask for the air miles when I check in, or I remember to ask for them but the airline then manages not to record them, or the check-in clerk informs me that I am not entitled to them. In January, on a flight to Australia — a flight for which I was going to get about a zillion air miles — the clerk shook her head when I presented my card and told me I was not entitled to any.

     “The ticket is in the name of B. Bryson and the card is in the name of W. Bryson.”

     I explained to her the close and venerable relationship between Bill and William, but she wouldn’t have it.

     So I didn’t get my air miles, and I won’t be flying to Bali first class just yet. Perhaps just as well, really. I could never go that long without eating.  
The narrator talks about flyer miles in this paragraph. Flyer miles refer to the travel points that you claim by flying through one’s privilege card. As explained in the earlier sections, with the points, you could buy more air tickets. But the narrator says that he never got his air miles because, as evident from the initial incident, he can never find the card in time.

The narrator was unhappy about losing travel points. While everyone he knew was travelling first class to Bali or around the globe using their air miles, he never collected any points.

One has to fly \(100,000 \) miles a year to use the card. But he has accumulated only about \(212\) air miles, despite having taken twenty-three airlines so far.

The narrator missed his points because he forgot to ask for the air miles when he checked-in. Or he would ask for the points, but the airline would fail to record them. Or else, the check-in clerk would inform him that he somehow was not eligible for the points.

So, the narrator describes one final incident to demonstrate his trouble with the air miles.

It was in January when the incident happened. He was on a flight to Australia, a flight for which he would get about a zillion air miles. So when he extended his privilege card to the clerk to register his travel, the clerk shook her head and told him that he was not entitled to any.

The narrator asked the clerk the obvious question: why? The clerk responded by saying that the ticket was in the name of B. Bryson, and the card was in the name of W. Bryson.

This part of the lesson is crucial because we learn that the narrator’s name is Bryson and realise that both the narrator and the author are the same. "B" in B. Bryson stands for "Bill", and "W" in W. Bryson stands for William. A basic knowledge on the author would make it clear that Bill is a short form of William, and that the writer is better known as "Bill Bryson" while "William Bryson" is his registered name.

Back to the lesson, the narrator tried explaining to the clerk the relationship between "B" and "W" in the names. But, as is the rule, the clerk couldn't accept it. Hence, he missed the points.

The narrator was obviously unhappy as he didn’t get his air miles, and he won’t be able to fly to Bali first class. But he concludes the lesson by saying that air miles may never matter, to begin with; because, if he had to travel, then the narrator would have to eat, and then he would have to relive through all those ordeals. And of course, he could never travel such a long distance without eating.
He could never take a long flight without eating
Meanings of difficult words from the paragraphs:
Air milesLoyalty points that could be redeemed for free flights
ZillionAn extremely large number
EntitledTo give someone the right to do or have something
National Council of Educational Research and Training (2006). Moments. Accidental Tourist- Bill Bryson (pp. 56-59). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.