I have two horses that are doing an occasional lesson now.
Rider doesn’t pay any additional cost. Horses are given credit per use (ie Bo and set an agreement on how much horses “earned” per hour.
In this case, Bo needed a couple nice lesson horses for an occasional lesson and I am welcome to help and observe lessons. Lessons are mostly just beginning walk/trotters and both horses seem to enjoy the lazy downtime and extra attention.
I would never hold the rider responsible for the bills as my horses have always managed to incur plenty of vet bills in turnout and I’m sure, knowing them, whatever injury would happen regardless.
Extreme case of negligence would be different, but simple walk/trotters I’m not so worried.