By "bear country" do you mean black bears or grizzlies? I would not take children in grizzly country (Yellowstone NP, Glacier NP). I would also check with authorities about bear activity. If bear encounters are happening in a certain area, I would avoid it. In the Sierra (black bears only) most bears can be avoided simply by camping in non-standard areas, well off trails.

I would not worry about a few food crumbs in pockets, but be more worried about overall bear-proofing/handling of all food and cooking. Store all food well away from the tent. If you wash up the kids (get food off their faces) before bed, you should be fine. Bears are curious about smells. I would not use scented soap or sanitizing wipes. You do not want to smell like a piece of candy after washing up!

Buy some OP (odor-proof) sacks to store clothing. I think they are about $10 for a package of three. If you cannot buy the locally (try sporting/hunting/fishing shops) buy on the internet.