I'm in the same boat as pretty much everyone else...
To answer the title of the thread, there absolutely is barn etiquette. To me, that means paying my bills on time, being polite to everyone and being respectful of their horses and property, keeping my space clean and putting away things that I use or take out. That doesn't include inviting people to ride with me.
Honestly, I'm a bit on the introverted side and, if I had been one of those ladies, I probably wouldn't have invited the other rider unless both I and they were alone. I don't want to step on any toes, after all.
I agree--definitely invite them to go on a ride sometime. That, for me, would open the door and make it obvious that they'd like my company. And, the next time, I'd return the favor. (:
The sensitivity of the internet baffles me.