You're over-thinking this and putting far too much thought into what another adult (who seems to not even be your close friend) is thinking about you and your child.
You don't even encounter them much any more. It's not like you're bumping into them all the time and the mom is saying, "Can Janie come over to play later? Why not?" Be glad that you're not in a situation where the other girl is always bugging your child to play (and then being mean to her) or you are constantly running into the mom.
Look into why you feel guilty when you did nothing wrong and neither did your child. There does not have to be some formal, official "discussion" to end a kid friendship and make sure all the adults are fine with each other. You certainly haven't been rude -- you haven't even interacted with them so you have not had any chance to be rude.
Did you grow up in an area where kids in the neighborhood were very tight friends and stayed that way for years? Or where moms judged each other on their kids' relationships? If so, that might explain why this means so much to you though you don't see them and your child is happy and has moved on. Something to consider. That's not your life now, so you can stop worrying about it.
Smile and say hi if you encounter the other mom and if she asks about the bus, tell her that it gives you an extra half hour not to take the bus. No other discussion of her kid's meanness on the bus is needed.