A tad long, but it's what I do I guess...
As others have said, bears regardless of grizzly or black aren't going to be an issue as long as you keep a clean camp. You can cook inside your hard shelled trailer (fan on even better), or outside, and eat inside or outside with no issues. Another reason for soft side being banned here is they retain cooking odors longer, not because they are less safe. If a bear wants in, I promise you, he is getting in your camper. The concern at FB is that there is a high concentration of bears in the area, and if people get careless and leave food out, one may stroll in, be redirected to the smelly morsel. They are opportunistic and once they learn there is an easily accessible food source, they will return. Once they return, they begin to get a little more bold and search more out since their go to spot is now gone. This is when it becomes more dangerous (mostly for the bear), so park officials will remove and potentially destroy the animal. This is because now the bear is habituated, starts to hang around, and because tourists don't all tend to use their heads, create a very dangerous situation. I was raised in Jackson, and worked in Yellowstone as well, and I can't tell you how many dumb things I have seen my years in the park. People chasing a bear camera held high, petting bison, walking up to momma moose with her two cute little calves (much more dangerous than a bear BTW), petting elk, approaching animals, you name it...
In all my years, I have had a bear in camp a handful of times. Every time was due to irresponsibility be it weak policies where there were no bear proof containers for trash, or one instance where someone else's cooler was left outside their tent. I did scare the bear away and when the people returned, showed them their demolished cooler. They left that night BTW, lol. This was the same bear that entered our camp on two sequential mornings as soon as my wife started cooking bacon. Funny actually as I blamed my wife's cooking, reminding her the nastier the smell, the more it will attract a bear, so it was her fault. I cook now, so I recognize that might not have been my best joke... Either way, I mostly dry camp and rarely do the campground thing. I have never, knowingly anyway had a bear in camp while dry camping.
Bottom line is if you are clean, you will be Ok Most animals in Yellowstone are so habituated by humans, they will stroll around in close proximity as anyone can attest especially with bison and elk. Bears are similar only in that they are aware of the human presence, and certainly live amongst the masses, but they are still withdrawn and will keep their distance. Actually, most people would be surprised by just how many are in the area, and how often they see you, but you don't see them. They certainly won't come knocking on the door when they know you are in your camper. Attacks on humans happen be it predation, but more commonly because you were a threat to them, their cubs, or their cache, but that too is rare and most often only because they were unaware of your presence and you startled them. Generally they just won't let you get that close and will move away without issue, often without you knowing they were there. Bottom line, if they know you are there, and you don't approach them, you will be fine. Don't worry about it, but instead enjoy the coolness factor of 10 in recognizing you are in a "wild" area they inhabit. Yellowstone is a little different with the amount of people, but the feeling for me when I see a bear in the wild, especially a grizzly is one that is hard to explain. It is the epitome of the wilderness that few people experience. Oddly the grizzly is my favorite animal and was actually my thesis in school. No, I am not Treadwell, who claimed to love the grizzly/brown, but was an utter fool in how he interacted with them and precisely why he is no longer with us.
All of this being said, with all my time in Alaska, Wyoming, Montana, and to a lesser extent Arizona, I have seen countless black bears and grizzlies/browns in the 30's while spending immense time in the wilderness. Only once did I have a scary encounter, and that was my fault since I was in a rush to get back to camp. I was walking quickly when I toped a ridge in Katmai when mamma and I both realized the other was there. She was about 30 yards away and immediately false charged, turning away about 10 yards in front of me with her 2nd year cubs in tow. I knew bears were very fast, but had a new found respect just how fast as I don't think I would have been able to get a shot off before she got me. I was just raising my .454 when she turned. That was scary and likely would have been a different story if had met her even 10 yards closer to the ridge... Either way, I didn't need a camera, as I will never forget that image...
In the end respect is good, but you don't need to be on edge while in FB. Be smart, take reasonable precaution and you will be fine.
