Calming other peoples nerves?

Okay, so here's the story. Today, I finally decided to take a family friend on a hack as I've been promising (and holding off) for a really long time. She has been riding for a while, mainly walk/trot, and on the same bomb-proof gelding. I put her on a mare that I trust fairly well, but she was swishing her tail and kicking a little at flies (I probably shouldn't have been so lazy and searched for the fly spray) so I guess that may not have helped her. So we were off through the trails. The trails are not scary whatsoever, we hadn't even started into the woods yet, so I really don't think that's what it was. We were about 10 minutes out, we had been trotting nicely, not even with too much speed. The mare has a decently smooth trot, so I don't think it was that either. She stopped out of nowhere, and of course then I did too. She asked me if we could turn back, so I said sure, figuring that we would just head back and ride around the pasture or the arena for a while instead. I don't even think I had turned all the way around before she released more than 1 bodily fluid. That is when I found out that she was EXTREMELY nervous, yet really good at hiding it. I got her off the horse, let her do the rest of her thing in the woods, then got off and we both walked on foot back home with the horses. While we were walking I asked her what was going on, she said she was just nervous. She didn't really specify any reason, but we both agreed to try riding again sometime soon. I really want her to be able to ride and not have her nerves bugging her so badly. Any suggestions? Also, anybody have any idea why she was so nervous this time? I've seen her ride before, she is fine on the usual gelding...

Too bad she did not tell you she was suffering so much fear. How awful!
I have fear sometimes , and I guess maybe you do , too. It's just hard for us to imagine how much fear antoher person might feel for something that to us is not big deal. I am oftern pretty scared cantering out in large open areas, but I bet many people wouldn't give it a thought. But I am usually ok with telling people the limits of my fear.

I can only guess that if you went out together again, that youi would want her to feel free to tell you how she feels and to set the limits on how far or how fast. It is very kind of yoiu to be willing to work with her.

Thank you!

This phrase mystifies me. Are you saying she urinated and defecated on herself out of fear?

As to the rest of your post, why wasn't she riding her own gelding? Couldn't she bring him?

It's not unusual for people who primarily ride only one horse to be nervous about riding an unfamiliar animal. They don't know the animal or its quirks, which can be extremely stressful.

If she wants to ride your mare again, I think you need to take it slow and let them become familiarized with each other. Have her do some ring work on the horse several rides before you go out into unfenced territory again. Being out in the open on a horse you don't normally ride can be very scary.

Well... I'm saying she had things coming from both ends. The gelding she normally rides isn't hers, I think it was her neighbors? I can't remember exactly. That sounds like what I'm going to need to do next time, start in the arena. Thank you!