I do outreaches with my local herp society. I didn't take my corns until they'd passed a year old and seemed pretty sturdy and well-socialized, but so far they do just fine for short bursts, and they don't seem to mind kids handling them. But I strongly suggest that if you're going to let your children's classmates handle one of your snakes, no matter how old, you have only *one at a time* out, and watch very carefully. I am never worried about the kids-- it's a corn snake, how's it gonna hurt them? But I do worry about my snakes.
As to transportation-- king-sized pillowcases are your friends. Normal-sized will work, but king-sized are much easier to tie off without worrying that you're knotting your snake up as well. Each snake of mine gets a pillowcase, and I put the pillowcases in a plastic bin with a lid so no one gets squished and everyone is centralized. The pillowcases seem to be very calming for them, since they block the light. And when a snake does still want to explore, it never fails to crack me up to see a pillowcase corner gently waving under its own power...
For ophidiophobes, and there will be ophidiophobes, one good way to get them less scared is to offer to let them touch the tail of the snake, and emphasize that you are keeping the head far away from them. (Yes, I know its teeth are tiny and nonthreatening, but they don't or they wouldn't be scared.) Once a scared person touches a snake, be prepared to agree that in fact they are not slimy, and isn't that interesting. If the spooky kid starts to seem interested, it's always good to get them to stroke the snake's belly as well, for the smooth texture.
Things people will say/ask:
"Is it poisonous?" (No, and it's not venomous either

)
"Where does it poop?"
"How big will it get?/How long will it live" etc-- basic questions about the species
"Does it bite?" I usually handle this one by pointing out that, while it *could* bite, so could the child's pet dog or cat, or even the child itself. But, I tell them, this snake is really calm and *won't* bite, and has never shown any inclination to bite. That's usually sufficiently satisfying to them.
"Does it have teeth?" I have no idea why people ask this so often.
Bonus: "Is it going to sting me with its tongue?" "Is it true that they only grow to the size of the cage you put them in?" (My answer to that one of late is "Only if you starve them.")
Especially for scared kids, it's always good to emphasize that they're brave for holding or petting a snake, and now they can tell their friends/parents/whatever that they held/touched a snake, and isn't that cool.
Not sure how useful this advice is to you, because the outreaches I do are generally less structured than an elementary school class, and I concentrate a lot on converting the ophidiophobes, which may not be a major focus for you. But hopefully this is somewhat useful, if long-winded. I love doing outreach; I find it really satisfying to know that I've helped a young person combat a foolish fear before it gets set in stone. (It may be even better to convert the adults, after the fear *is* already set! We have people cry with the release of getting over their fears the first time they touch a snake. It's really, really powerful to be able to help someone cry in relief and happiness, and know that you have really and for true changed their life for the better. It's a great feeling. Man, now I wish we had another outreach scheduled soon!)