Well, when it came to me organising my own school trip which involved a 8 hour coach drive up some very mountainous terrain, I decided I would be fully prepared for the worst. Of course I reminded students and parents that travel sickness pills might be an appropriate idea as well, but just in case, I designed and created the "Sick Kit"!
(P.S. plasters / band aids aren't technically related to the "sick" bit, they're super handy to carry around!)
It's so easy to use: after the child has done their thing, simply pop on a pair of disposable gloves, take the paper bag from them and put it into one of the plastic bags. Hand them a disinfectant wet wipe to clean up and toss that in the bag too. You can then keep all these bags in another bag or bin liner until your next stop. No mess, no fuss, no embarrassment. Worth every penny.
So, next time you're on a school trip (especially a coach!) consider preparing your own "Sick Kit" alongside your First Aid Kit - I can promise you it will be worth it!