I'm looking for a science-fiction story I read a long time ago, probably in the 1970s but maybe later. I believe it was a longish short story.
The Generic Plot: A girl (teenager?) lives in a stereotypical domed city that is over populated and it feels way too much like living inside a giant machine. Everyone knows there is nothing beyond the city and this life is all there is, but she instinctively wants more.
Important Identifying Elements:
1) Because the population is so dense no one ever speaks to anyone else unless they have to. Doing so would be intruding on their space. And everyone is very careful to never touch anyone because that would be horribly rude.
2) Key Phrase: "I trespassed." If they touch someone accidentally, they apologize by saying "I trespassed."
3) Key Scene: Even within a family, intimate talking and bodily contact is frowned upon, but there is a crack between her bunk cubical and her brother's, which lets them secretly whisper back and forth to each other at night.
4) Key Physical Element: The city has a computerized transport system consisting of small cars on rails. You get into a car, punch the number code of your destination into the control panel, and the computer routes you onto the correct rails to get there.
5) The Most Important Plot Element: Whenever she is mad or frustrated she jumps in a transport car by herself and punches random numbers over and over so she can ride back and forth all over the city in splendid isolation. One day after a big fight with her parents she does this and the car goes through an opening in the dome and stops in a wide open space that is lush and green. What's more, almost no one else is there and the people who walk past her politely nod and say hello. After while she excitedly gets back in the car and punches in the number for her neighborhood, eager to tell her family what she's found. It's only as she's arriving back home that she realizes she doesn't know what random number took her to that wonderful place, and the story ends with her spending every free moment riding around and punching in random numbers, hoping that one day she'll randomly discover the number that takes her back there.