I have experiences like the one the letter writer describes in my own past as well. Definitely more than one, and about more than one issue (racist, homophobic, trans-phobic, able-ist etc.) the further back I think, the more I find, and the worse they get. If I let them, things I said when I was twelve will echo around my head until I wonder why I ever open my mouth to begin with. I honestly think that to have memories like that is the norm.

I would be genuinely surprised if the friend you describe doesn't have a handful of micro aggressions to her name as well. While this is no excuse to continue to perpetrate such incidents, it might make it more likely that this particular memory doesn't cause her the same pain that it does you. At this point, only you know what you said, and whether it was an isolated word vomit style incident, or only the worst of many things you might have said or done.

If you have genuinely been a strong and admirable friend to her over the years, then chances are those are the qualities she remembers when she thinks of you. To suggest that a person you were living with, who is or was close to you for an extended amount of time, has been secretly holding on to one terrible offensive joke you made seven years ago is kind of arrogant on your part. Is she hording offenses like a dragon with pile of gold? Give her the benefit of the doubt. If she chooses to continue your relationship now that your shared habitat no longer demands it, accept that she has chosen to overlook it. Recognize that to bring this up out of the blue would be for your peace of mind, not hers. Instead strive to do better and be better in your interactions with her.

Maybe it will eventually come up and be resolved to the satisfaction of all parties, but until then, don't tell her you're better now, show her.