momz,
I have some experience camping in bear country in the Rocky Mountains. I've taken Boy Scouts to Philmont Scout Ranch in northern New Mexico and bear policy is ingrained before we arrive, once we arrive, and while we are there. There it is the Brown/Black Bear (don't know what type you have at RMNP). The species is the Black Bear but his fur color is brown for the most part (the two are not to be confused).
The thing about the bear is his nose. Yes, his nose. His sniffer is VERY sensitive and it is directly connected to his stomach. So I would say this:
1. As far as your tent, no food, snacks, or delicious odors AT ALL inside the tent. No granola bar before lights out, no Gatorade spilled on the tent floor, etc. Take your toothpaste out at night and lock it in the car. Same for bar soap - shower/bath in the mornings not the evenings ("let's wipe a DIAL gold bar on my body which smells great and lie down in my sleeping bag"). Or at least not right before bedtime - leave a few hours between shower and lights out.
2. Pots, pans, silverware etc. that have been cleaned can be left outside overnight assuming they have been cleaned/sterilized. But put them "way out there" somewhere. Not near the tent. Over on the picnic table or further away.
3. Your phrase "chuck box" is, I assume, your stored food or other pots and pans with accessories. Any FOOD even if bagged/sealed/boxed, crated is still fair game and should go in the car every night or in a locked National-Park-approved bear box. Other pots, pans, spatulas, bowls, plates, etc I would leave in the car if there is space or outside and unlocked. The worst that can happen is bear slobber on them. A lock on it will mean the bear will keep after it until he peels it open and wrecks things. They are stubborn and persistent that way.
4. Stoves and things you might leave out is up to you. My Coleman 2-burner stove has slight spills and stains on the silver cook surface under the burners. That could produce an odor. I would ALWAYS err on the side of safety/caution and when in doubt, lock it up.
When we camped at Philmont, we hung a bear bag in the trees WAY up high about 200 yards from our tents with all our dehydrated food items, toothpaste/deodorant (odorless of course), and plates/sporks. I have had bear encounters that still curl my toenails to recall them.
The sad thing is if a bear gets into your food or items, he's learned to associate people with food. So when he sees people he will come whether he smells food or not. He might at best get trapped and relocated one time but if he becomes a repeat offender, he's as good as dead. It will come to that. If it's YOUR food/smells he found, CONGRATS! You've signed a bear's death warrant. Not kidding.
So as I said, err on the side of caution. Use common sense. If stuff is sterilized, clean, or unused, leave it out but far away. If there are odors or real food, lock it up.
Save a bear's life. No joke.
Bama Ed
PS - I've had two significant bear encounters. The first, 36 years ago, the bear got our bear bag (smells) and punctured every bag and sampled/licked/ate every item in it. The second time 9 years ago was when during a lights out check, we discovered a boy with an open granola bar half eaten in his tent. He went up the hill to the latrine to throw it in (thinking the latrine smells would overpower the granola bar smells since the bear bag was already up in the air) and saw two red eyes motionless watching him in the dark as he did so. Our boy turned his back and walked down and the bear followed him down the hill into our campsite/fire area. It was scary as hell. We drove him off with rocks, whistles, thrown sticks, and luck. But then the paperwork was like,
"Oh snap, how many times to I have to tell this story?" 