I was 12 when I set off for Germany on a school exchange. It was common practice at the Rudolf Steiner school I went to for children to spend a term abroad and so, without any real idea of what it involved, I volunteered to go. The family who took me lived in the south of the country, in a village outside Ulm, and they had eight children, including a girl my age who was to stay with my family, in my room, while I was away.

The Schulze-Schildorfs met me at the airport. The father was huge, with a bald head and an enormous stomach, but he smiled at me encouragingly while his seven remaining children, aged four to 17, told me their names. The mother wasn't there. I soon discovered she was ill, in hospital – we'd visit every Sunday – and although I never discovered what was wrong, she remained in hospital for the whole three months of my stay.

The Schulze-Schildorfs' house was on a hill on a small modern estate, with a bedroom upstairs for the parents and four small rooms with bunks for the children below. I shared a room with my exchange's 10-year-old sister, and went back and forth to school with her on the bus. But what no one had warned me about was that in the south, people spoke Schwäbisch, a local dialect, and although I'd been learning German since the age of six, I'd been learning Hochdeutsch – high German – and couldn't understand a word of what was being said.

"Hochdeutsch bitte," I'd say pleadingly as I sat at the table – a woman from the village came in every evening and cooked supper – and for a few minutes the family would stop talking in what was probably the equivalent of Geordie and break into their version of RP. But there was something else that I needed to say, and it took me a few days to pluck up courage: they had my name wrong. They thought I had the same surname as my stepfather, who'd organised the trip – and there was an uncomfortable silence when I told them what it was.

"Are you Jewish?" the father asked me quietly, and never having particularly thought I was before, I nodded, yes.

By the end of the first week I was painfully lonely. I'd brought three books with me and I was close to having read them all, when a letter from my mother arrived. The glory of it. The pleasure of reading and re-reading her words. I wrote back that night and waited; and then, unable to bear the days that passed, I wrote to my stepfather, my grandparents, my sisters, individually and in pairs. I wrote to my neighbours, my class teacher and my father, who'd been unable to understand why I was being sent to a country that his own family had fled from when he was my age. I told him it was all right. Apart from the Schwäbisch, it was fine.

Soon I began writing letters to people I hardly knew: "Hello, you may not remember me but…" Before long I'd accumulated such a large circle of correspondents that when I arrived home from school at the worryingly early hour of 2pm, I could slip my hand into the post box and there would be at least one letter to see me through the afternoon.

And then I made a friend – a pretty, blonde-haired girl called Julika who lived near the school, and I began to spend all my spare time with her. Her father was a teacher and they spoke strict Hochdeutsch at home, and although I was slowly mastering Schwäbisch it was a relief to be able to join in their conversations.

Spring turned into summer, Julika and I both turned 13, and we spent afternoons at a vast lake outside the town, swimming, chatting, chasing each other, talking about music and boys. I still wrote my multitude of letters, but my homesickness had abated and I was happy.

Then another girl from my class, Astrid, asked if I'd like to go back to her house the following week and stay the night. "All right," I agreed. It wasn't so much that I wanted to. But I was curious. And polite. The day we agreed on coincided with a school trip. We took a train into the country and went hiking through a forest. We had a picnic and, on the way back, as Julika and I talked and laughed, I caught sight of Astrid, walking behind, alone. "Oh God," I told Julika, "I'm meant to be going to her house tonight," and Julika grimaced.

There were many goodbyes to be said at the train station in Ulm. "Bye," I shouted as Julika climbed into her father's car and I waited on the steps for people to disperse so Astrid and I might find each other. Cars sped up, children were whisked away, teachers vanished, commuters climbed aboard trains. I felt sick at the pit of my stomach. Was it possible Astrid had gone without me? I remembered the glimpse of her face on the long walk through the forest. If she had forgotten me, I told myself, surely she'd remember, or her mother would, and I imagined their car screeching to a halt, drawing up at the kerb.

I waited an hour before giving up hope. It was evening, the commuters had thinned out and my family weren't expecting me home until the following day. They had a telephone, but I had no idea of the number.

Across the road from the train station was a bus station. There was no one much there, but eventually I ran over to it and began to scour the information board for a familiar bus. I'd been used to taking the bus home after school, but this station was on the other side of town and I didn't recognise any of the stops. Then a car pulled up by the train station. What if it was Astrid and her mother? I raced back across the road only to see a man get out, wave, and hurry off.

Another half an hour passed. If Astrid was punishing me for not talking to her, surely she'd punished me enough? Or her mother would realise what was going on and force her to come back. I tried the bus station again, but this time I returned to my look-out on the steps even more quickly, terrified that I had missed them, convinced they were on their way. I must have run back and forth at least 10 times, scanning the timetable, panicking, rushing back across the road. All the while hating Astrid with a pure, cold hate.

Then, as evening began to turn to night, I saw a familiar name on the front of a bus. It wasn't the name of my village, but it was one nearby, and I got on just as it was about to pull out. I dug in my pocket for some change. The fare was more expensive than from school and I was told I didn't have enough. "Half," I tried then, "I'm 11, I'm only 11."

When the driver looked at me and shook her head, I turned to the other passengers and, digging my nails into my palms so that I wouldn't cry, I called to them. "Won't any of you help? This is all the money I have and I need to get home." Not one of them met my eye. "What's wrong with you?" I shouted then. "Why won't any of you help?" My face was burning and reluctantly, embarrassed, the driver nodded, the doors swished closed, and I was on.

It was a long walk along the main road, and it was dark when I arrived home. The family were in the living room, the little ones in bed. They all looked up at me, surprised, as I came in. "I… I…" my lip began to tremble, and the big bald father held out his arms. "Meine kleine madlie," he said in his broad Schwäbisch – my little girl – and he pressed me against the hard dome of his stomach and held me there while I sobbed.

The next day nothing was said between Astrid and me, but the following week she approached me and asked if I'd like to come and spend the night at her house. I looked at her. I'd changed in the last week – I'd shouted at strangers in a foreign language, cried in the arms of someone else's father, saved my own life! – but I was still curious, and unnecessarily polite. "OK," I said, "I will." I knew that whatever happened, from now on I'd be all right.

Esther Freud's latest book Lucky Break (Bloomsbury, £11.99) is published on 4 April