The first one is somewhat odd. Saying "Good-bye" happens in an instant, in a moment. "for one year" expresses it happened more than once, notably for a long period of time, one year, they stood there saying "Good-bye" to each other. Try,Originally Posted by namsteven
We said good-bye a year ago.
It's been a year since we said good-bye.
As for the second one, why not try,
We broke up a year ago.
We have been broken up for a year now.
- For Teachers