It was mid-winter in early July and I was stranded in Buenos Aires. Jet-lagged close to the borders of hallucination, I had pitched up in the city of Jorge Luis Borges and Diego Maradona as part of a foolish, month-long hurtle around the planet.

The journey was for a book I was writing about the World Cup, the plan being to watch as many people in as many countries as possible watching their teams on television. I'd visited 10 cities on three continents in three weeks. Everything was going swimmingly ... and then I reached South America.

Soon after I landed, Argentina's football team lost to Germany. Then Brazil, my next scheduled stop, saw its team lose to France and my arrangements were in tatters. I needed to get back to Europe, but changing my ticket was impossible. I would just have to spend a few days here in the city with the world's highest per capita number of psychoanalysts and plastic surgeons.

At this point, my knowledge of Buenos Aires consisted almost entirely of cliches and useless fragments. For instance: the city produces many of the world's most talented footballers. It invented tango. It is the 'Paris of South America'. Above such trivia was the reputation of the city's defining genius: blind Borges, fabled creator of labyrinthine stories and dreams within dreams. I knew little about Borges but soon discovered that he grew up in a house near my hotel in the fashionable Palermo district.

I floated in the magical city, drifting from one district to another, walking, taking buses and trains, admiring the Manhattan-style boulevards, jalopies and fruit shops. I got lost in an infinity of back streets, was discomfited by the aching poverty of unfashionable areas. I entered candle-rich churches, tripped on broken paving stones in streets for the wealthy. I sat in parks and cafes, discovered an old battleship, watched an endless flow of sad and beautiful faces.

Then something trivial grabbed my attention. Elsewhere in the world, the buses of capital cities tend to stick to predictable and reliable routes. This is a good thing and helps tourists not to get lost. But each time I took the number 128 it seemed to go somewhere different. It always followed the same general trajectory, but there were odd little variations, a stop missed here, a new turning there. There was surely a simple explanation: the one-way system, perhaps, or roadworks. Maybe I'd just imagined the whole thing.

Soon it was my last night in the city, and I spotted a 128 heading towards me. I decided to devote my evening to solving the puzzle. I would ride the bus 'all the way to the end of the line, baby', like Phyllis and Walter in Double Indemnity. I didn't care about the journey. I just wanted to know the destination. I'd sit on the thing until it reached its final stop. Then I'd sit on it some more as it trundled back. And then I'd know.

The bus was green. Or red. Or blue. I forget, or maybe I never noticed. I put my pesos in the antique machine to buy a thin paper ticket and sat near the driver. Clanking and grinding, we pulled slowly out of the city centre. It was too dark to see much through the big windows. Presently we reached a wide and seemingly endless cobbled street in an empty industrial district. Later, there were traffic lights where poor children played a game involving old tyres and accosting passing cars. Soon, I felt sure, we would reach the last stop. Hand-scrawled street signs began to replace printed ones. Had we travelled an hour? An hour and a half? More? I'd lost track. The original passengers left. Others got on. We came to a narrow street with cafes, neon lights and fruit stalls. Was this the terminus? No. Just another stop.

Relentlessly, the bus barrelled into the night. I was getting anxious now. I worried about not getting back to the city at all, about missing my plane in the morning. I wished I spoke Spanish. Using a combination of pointing and bad Italian, I finally asked the questions I should have asked at least an hour earlier. Where exactly was the final destination? And how long would it take us to get back to the city? The driver shook his head and simply pointed ahead: 'No. Not stopping. We don't stop.'

What? The driver pulled over. He wrote directions on a scrap of paper. To return to the city, he explained, I must get off at the next stop and walk to a large road with many trucks. There I would find a bus stop beside a closed cafe. I must take only the green bus. This point he emphasised: 'Green. Green.'

I did as he said. Amazingly, it worked. By midnight, I was safely back at my hotel on Malabia Street. Along the way I passed Jorge Luis Borges Street. Only much later did it strike me that my bus was a metaphor on wheels. Maybe this was what it meant. Time flows only in one direction. Life does not do return tickets. We may know our way, but a journey will always take us somewhere unexpected.

But it couldn't be that simple. For one thing, Borges didn't believe in linear time. He wrote paradoxical stories folded back upon themselves and expanding to the infinite. His is a bewitching realm of symbols, and fictions truer than truth. 'Imagination is the thing,' he once said. 'I try not to be true to things actually happening but to my particular dream at the time.'

In one of his best known short stories - 'The South' - a thinly disguised version of himself, a librarian called Dahlmann, accidentally bangs his head. The wound becomes infected. He nearly dies of septicaemia but recovers and leaves Buenos Aires for a journey into the countryside. Dahlmann gets thrown off his train, runs into some gauchos and is challenged to a knife fight, which he accepts. The story closes with him, a frail city man, knife in hand, walking to certain death. Beneath the literal facts of the journey, said Borges later, was a different interpretation: everything that happens to Dahlmann after leaving hospital may be his hallucination as he lies dying in the hospital. It is a fantastic vision of how he would have chosen to die.

I left Buenos Aires next morning, returned to Europe and wrote my book. Perhaps more importantly, I discovered the world of Borges, which is as compelling and seductive as Buenos Aires itself. As to the bus, I'm pretty sure it just kept going. It must have chewed through rivers and mountains and rainforests, headed into Uruguay and kept moving. It's probably in Canada by now. Catch it if you can.

David Winner's book 'Around The World in 90 Minutes plus Extra Time and Penalties' is published by Bloomsbury at £6.99. To order a copy for £6.99 with free UK p&p go to observer.co.uk/bookshop or call 0870 836 0885