Yes, in light of the additional information, a text to the old trainer saying something like “Have missed seeing you and x, y and z horses. Wanted to let you know that I’m taking lessons/leasing a horse at a barn closer to my college, the shorter commute means I’ll be able to ride more often. Thanks for all your help with my riding, hope everything’s going well for you.”
I think old trainer will read this text, think “Oh, cool, that’s what happened to her. Good to know.” and go on about her day.
Maybe, just maybe, old trainer will text back and say “Thanks for letting us know. Good luck with your riding!”
In re: my above story, the instructor I mentioned, who became my mentor, was pretty much my model for how to be a decent human in the horse business.
If she saw a former student or client at a horse show, she would make a point of speaking to them and saying something nice about their riding or the horse they were on. Students come and students go, but a reputation for being polite and professional is forever.