I've been trying to "radiate" confidence for my older rider. If she bounces at the trot and asks about her position, I tell her how she's bouncing a lot less than the first times (which was very
true), how I used to practically bounce right
out of the saddle, and then I'd talk about riding with her legs more. A lot of the beginner students, when they push down on their feet, send their legs waayyyyy out there, so they can't get a foundation on their horse's side (especially at faster gaits), and it causes them to bounce.
The same older rider would bounce some days more than others. I shrugged it off and told her we all have our "off" days, even me, where our position is lacking. (Usually when we're distracted by home problems, a huge pesky bill, etc.) Then I tell her to focus on the task at hand -- nothing else -- and try again. At one point I explained:
"When I first began to ride I was so focused on my position that my focus ruined my position. I thought so hard on "heels down, eyes forward, legs squeeze" that I overdid it. When I finally had enough of over-thinking I focused more on my horse -- and I stopped bouncing."
The younger rider, I recently came to find, is insecure because of her mother, who watches from a distance. She told me her mother is overly-critical and it worries her; she wants to be great but is afraid to fail. I waved my hand at this and said, "You're on a horse riding by yourself! Why does she matter right now?" That seemed to help her, and she's slowly been coming out of her "shell."
My biggest fear is building this course, and then finding out their major slacking points too late! I don't want to set up a "medium" jump (around 1'), thinking they're capable, and then have their horse jump and them find their way to the ground. We use old fence poles for "Cavalettis," but most of the horses just do a hop-skip-jump over them, not really a jump. I still try to teach them jumping position, though.
I want them to be safe, confident, and still have fun.