Yes, there are Polar Bears in the region of King William Island. Maybe not as densely populated as in other arctic areas, but they are there in number. After flying and hiking in the wilderness over the years, I have had a few bear encounters. And from my direct experience, the bear to be most respected -and avoided- is the Polar Bear. Polar bears are not like other bears.
Overview of the different bears (my own opinions):
Black Bears:
Black bears are the smallest in body size in general. They are mostly scavengers and seem to act like giant raccoons. Typically very fearful of man, except where conditioned by humans - where given free food handouts and/or experiencing high human density habitat and encroachment there of. These bears are mostly cowards. Even a black bear sow with cubs will many times run from a confronting human. However, they should be respected, because there is always a few exceptions to the rule, and there have been attacks, and even deaths.
I have never had a scary situation with a black bear.
Grizzly Bears:
I put them in two general categories - (1) Grizzly - Inland bears, smaller (2) Brown - same as a Grizzly, but coastal and much bigger.
These bears, somewhat like the black bears, also tend to shy away and avoid humans, if they feel that they can maintain their self esteem in doing so. They do have more "attitude". They are bigger than black bears in general and the same escalation can be given to describe their overall stubbornness and aggressiveness. Grizzly sows will many times not run when surprised, or even worse, when cubs are threatened. If you were hiking and would happen to hear the squeal of a Grizzly cub, get ready because you will probably be in a world of hurt within seconds.
My experience in direct close encounters with the Grizzly has been neutral with OK outcomes.
In Alaska, out on the peninsula, north of Kodiak Island, I was in an awkward position once while bent over caping my caribou kill. In this territory, when a gun is fired, it is like the dinner bell for any bears within earshot. So after an hour or so, a very large dark furred Grizzly came to within 20 yards before I noticed that he was there. But his manorisms did not indicate aggressiveness; no gnashing of teeth, no swinging of head side to side, etc. So I promptly lifted what free parts of the caribou I could, then I started to whistle as calmly as I could muster. And then I finally picked up my gear and rifle (all in about 30 seconds). And then I walked away slowly - BACKWARDS. The grizzly just stood there and looked at me as if he were telling me that I should leave now. The hunting group came back the next day and from 200 yards away all could see that same bear - and he was jealously guarding the kill site. Now you could expect he had a different attitude, it was his property now. When he stood on his hinds and started sniffing the air currents, everyone crept away.
Polar Bears
Cute? Yes. Cuddly? NO.
The polar bear is the most dangerous and deadly of all bears, and they do go after humans. They stalk. And we are on the list. They are meat eaters and hunters and live mainly on seals and whales. They are experts at patience and stealth. These bears will sit patiently over a seal breathing hole in the ice for many hours in a row, motionless, even slowing their breathing down, in cold weather many degrees below zero. They are on average much larger than any bears on the planet.
I have had some slightly unnerving situations with polar bears.
I first experienced polar bears while flying up the Hudson Bay coast from York Factory at the confluence of the Nelson and Hayes's Rivers, up and around the Cape near Churchill. This has the highest density of polar bears in the world. My immediate thought was "Wow, all of these bears are huge, there were no small ones." Many are close to or over 1,000 pounds.
Seeing polar bears in small groups, I noticed a pattern in their behavior to be a little curious of me, but keeping their distance and not confrontational. They were probably mostly females. The lone polar bears are the ones to watch out for. And the young adolescent ones especially. Males.
My first somewhat unnerving experience was when I landed in the partially melted ice pack of Hudson Bay, in open water, to view a nice sized polar bear on the other side of that ice flow, maybe 1,000 yards away. I moored the seaplane and was out on the ice within minutes, but then couldn't see the bear anymore; he had gone. I knew it was time to leave and sure enough, after I took off and circled the plane overhead, I could see that the polar bear had closed almost the entire distance by swimming in the water cunningly on the pack edge - the bear was almost to where the position my anchor had been clawed in the ice.
Another time, in 2003 (video clips online here) after a forced landing, a polar bear was sniffing around closely within 2 hours later. When this lone bear came, it was with a meandering zig zag path, like it was unaware of my presence, never looking, seemingly distracted, but ever getting closer. This is how they stalk sometimes - arctic summer; no ice, no cover. Best to sit on top of plane, not inside. Was picked up by search and rescue, so avoided a total confrontation.
Also in that same week, just to the north while there, an Inuk grandmother was devoured almost whole by a 2 or 3 year old polar bear boar. The small grandchild in the tent was initially confronted and the old woman took a broom and beat on the bear's back in order to divert the attention away from the child. I also still carry a newspaper article of the unfortunate Inuk hunter who, that same month, at his tent, was partially skinned alive by another polar bear, which was fortunately dispatched by his fellow hunters.
So, to conclude - Polar Bears do come to you.
Best defense of bears, in order of least aggressive to most aggressive:
1) Bear spray.
2) Cracker shells - Silencers from a 12 ga. shotgun, with an explosive (like an M80) that has a delayed fuse. But one has to be careful as sometimes it can explode behind the bear and scare it towards you. Not good.
3) Slugs - In the the shotgun's magazine, in line behind the cracker shells.
4) High powered rifle. A last resort and it better be big. I carry a .460 Weatherby (500 grain bullet traveling at around 3,000 feet per second - good on Cape Buffalo and Elephants).
Oh, and by the way, if you think you can just go ahead and shoot a charging polar bear, try not to because you will be in big trouble with the law if you injure or kill one. You see, it's your fault.......because "you were there." Just know the consequences before you pull a trigger.