Cooking and eating a ways from your shelter is a good idea and if you carry a base layer dedicated to sleeping in you can change and hang your clothes you cooked in, in your food bag, or store them in a bear container if the camp sight has one. That would be going the extra mile so to speak. Not a bad strategy for brown bear country. Having camped in brown bear country we have done just that. Put snack wrappers and smelly trash in a separate trash bag instead of putting them in your pants/shirt pockets or in hip belt pockets. Don"t wipe smelly hands on your pants. All just common sense stuff. No pun intended.

Last year in NC, the Smokies a 16 yr old was pulled from his hammock while camped out with his dad by a black bear. The boy remained conscious during the attack as his father chased away the bear but sustained lacerations and head injury. By reports I read their food was properly stored. I don't have any other details. So even black bears are not all the cuddly, more scared of us than we are of them type. Statistics show attacks are very few but they DO happen.

Teach your kids good food practices BEFORE they go on their first trip and the importance of doing so. Giving them a chance to "train" for the event could be fun and rewarding for them. Also teach them about good human behaviors if encountering a bear on the trail or in the woods like not running is a big one. It takes a bit of being good under pressure and discipline to hold your ground. Easier said than done. IMO if they are not old or mature enough to understand why its important they may need a few more years. You sure as heck don't want them to be scared of sleeping in the woods.

All of life's activities come with some sort of risk. I would sooner take a teenager on the trail in bear country than let her/him drive my car but in the end you have to access the risks for your family.

Edit = and remember its not a race to see how young kids can do stuff. Life makes time for the right time if you know what I mean.