No problem with wandering away as you aren't allowed off the buggy till your are back to the embarkation place. You definitely do not want to put your hand out the window as they WILL bite it right off!!! and if not then the leader will actually kick you out of the trip and take you to the airport and send you home.
Even within the town of Churchill there are 'off-limits' posted areas depending on the time of year. Heed them. Having said that, there's a Russian biologist who works - alone - on an island with polar bears and all he carries is pepper spray. He's only used it once in 25 or so years, on a large boar that literally backed him into his trailer. It's a matter of being able to read them, what their intentions are, etc. They're not mindless monsters, just top level predators. When I worked with George Kolonosky (renowned bear biologist, retired), he always said, "Black bears will run from you, polar bears will try to eat you and grizzly bears you can never tell." All the years he worked with black bears he never carried a rifle - only an axe. With polar bears it was different.
I went up there once in July to photo the Belugas and as it was summer, the tundra flowers were out in full bloom. So.. there i am with a borrowed van wandering out on the tundra photographing the pretty flowers and when I get back into town, I'm asked if I saw the polar bear wandering out on the point!! Thanks for telling me about it AFTER I get back!!
Case in point! And polar bears basically starve throughout the summer as without the ice they can't hunt seals. With the rise in ocean temperatures the ice is coming in later and going out sooner so there are fewer months of the year they can hunt. Of course if you go back a couple of centuries there were once polar bears down as far as the mouth of the St. Lawrence River so they may have to adapt to hunting on land.
The closest I got to a Polar Bear as when one came up under the back deck of the buggy and was snuffing our feet thru the grate. Sooo.. I laid down on the grate and blew into its nose and it sneezed into my face!! Not a pleasant smell, I can tell you.
Given their diet, can you blame them?
There was a Canadian Wildlife Service study a number of years ago to determine a bear deterrent for polar bears. They basically set up a gauntlet or fence wire, barbed wire, electric fence, loudspeakers, rubber bullets... at the end of the gauntlet they built up a fire and laid some seal blubber on it so the smell would attract the bears. A three-year old, sub-adult male caught the scent and went through the entire gauntlet as if it was smoke. He didn't stop until he got to the blubber.
Mike.
P.S. For the Inuit, pre-contact, hunting polar bears was a dangerous occupation. One technique was to take a piece of whalebone that was flexible and sharpen both ends to points. Bend it into a 'U' shape and shove it into a piece of blubber, then hold it until it freezes. Find a polar bear and leave the bait for him. When the bear swallows the frozen mass, it slowly thaws out in the stomach. When the blubber thaws the whalebone expands. Follow bear until it bleeds to death internally. It sounds cruel, but it was one way of living in a very harsh environment.