Hello there,
Good on you to help out with this class! To address your questions:
Is it safe to take her?
Short answer: Nothing is safe, but yes. Since you describe the class as "zoology" I'm guessing it's for secondary school and beyond, not rambunctious kiddos? Provided these are sensible and respectful adults or soon-to-be adults it's probably safe enough. Do be careful though if she's to be in close proximity to an adult bearded dragon - they can be both territorial and prone to eatting smaller lizards.
Will she get stressed out?
Short answer: Almost certainly. However this depends a lot on the temperament of the dragon and what's going on otherwise. For instance, my boy Guac shows little to no signs of stress during travel. I have seen some dragons though that get quite upset, but honestly I doubt any lasting harm is done. What your describing is probably no more stressful than a vet visit, after all.
What should I take her in?
You want to treat this similar to if you were shipping her. Primarily, ensure a rigid, securely closing carrier with plenty of air flow. The container should be as small as possible to reduce the risk of the animal sliding around inside the container while allowing the animal ample breathing space and some ability to move around for comfort. You also want a clean, absorbent material in case the animal defecates during transit, paper towel works well - bring spare if you can! The final consideration is opacity - clear containers are better for letting you check in on the animal, while opaque ones are likely to keep the animal calmer. The best solution I've found is to use a clear container for the animal and put that container a secondary opaque one.
For my roughly 18 inch boy, I use one of
these with about 2-dozen air holes drilled into the top and sides. Since the container is 14 inches long, Guacamole's tail has to be curved for him to fit in it and he can't slide more than an inch or two in any direction, but he can easily walk around in a circle inside of it, even with a layer of fleece or paper towels beneath him. Finally, this usually is put in an opaque secondary bag. For lower temperatures, with an insulating but air-permeable material placed above and beneath - my go to is folded towels or a throw blanket.
A good alternative is a cotton bag or pillow case tied closed at the top so she can't get out of it placed inside of a closed Styrofoam cooler with air holes punched into it with a pencil or similar-diameter object.
Is temperature a concern?
Yes and no. So long at the Bearded Dragon's body temperature stays above 55 degrees Fahrenheit, she will suffer no long lasting ill effects. Ideally, you want to keep her temperature at least 70 degrees F or above. The temperatures you are estimating inside of the building are absolutely no problem - My house is about 70 F at night and my parent's house about 65 F at night and Guacamole has never had any issues with it. However, you need to be very careful that she is not exposed to the outside air for very long at all.
If she needs to be out of her travelling case in 33 F, I would just flat-out pass on this adventure because it would be too risky for me. However if you can make sure she remains in her travel container inside an insulated bag or wrapped in a blanket, towel, or coat during the period of time you'll be outside (and that period of time is relatively short), you should be fine. It she's at 70 degrees F or above, she can stay that temperature for up to a day or two without any serious complications (assuming her health is as good as you claim it is).
If you want to provide her a heat source during travel, consider getting an oxygen-activated heating pack. If you do this, DO NOT use hand warmers! They get too hot and are a very big risk. Instead, use the kind meant for shipping live animals and plants with, like a uni-heat multi-purpose shipping warmer.
For more information, try checking the following links:
Ship Your Reptiles - A website dedicated to helping people safely ship and move reptiles.
Travelling With Reptiles - Youtube Video by Snake Discovery, a channel run by Emily, a exotic animal educator with a degree in Fisheries & Wildlife.
How to Travel with / Transport Reptiles in Your Car - Youtube Video by GoHerping, a channel run by Alex who currently is one of the people running
Emerald Scales which rehabilitates and rehomes animals.
I hope that helps and I'm happy to answer any further questions!
-Ellen