I think if you get hired at the grocery store and you run into them - just act pleasant and normal. If you run into her dad you might want to mention that you hope this won't affect your business relationship - if he's down to earth he probably won't let that happen.
If you want to write her a note, it's probably best not to take the tone that you're not blaming her, where she will then become defensive. It's not that either one of you is really at fault, rather you both are just miss matched for each other now. She's dominant and you're more passive but learning or wishing to become more assertive - which doesn't agree with her. Relationships evolve and grow - which means sometimes it requires a parting of the ways. You were fine at first with her, but you're growing up and your needs are different and it was taking too much energy and work to maintain the friendship. Perhaps you needed this experience to learn that you really need to think for yourself and be assertive.
You could say something like I don't want us to be bitter and I don't want you to wonder why the friendship has taken this turn. I value the friendship that we had, but unfortunately because we've both changed, it has become unbalanced - where you no longer feel it's healthy for either one of you.
I hope though that if you do see her that you both won't ignore each other because that's uncomfortable for you both. You can still be polite and maybe one day be friends in a different more balanced way than before.