There have been several accounts where the bear is wounded and then runs off.
I suspect most polar bear attacks are predatory rather than territorial.
Would you feel adequately armed in polar bear country with a .243 Winchester? I know you are all about being prepared. Would you really feel prepared for an up-close encounter with a polar bear defended by a .243?
The Svalbard standards call for a rifle that can deliver 2,700 joules of impact at 100 meters. The .243 delivers just under that at the muzzle. The standards also call for a 11.5 gram bullet, at minimum but the .243 maxes out at 6 grams for commercial loads. A .243 is not going to have much of a wound channel. From what I have read, polar bears are undeterred by warning shots because the cracking of ice which they hear all the time is like a rifle shot, so they don't associate it with danger. So, it's probably going to have to be the wound that deters them so I'd want to send them a VERY clear message that continuing this is not a good idea (and if things go right, it's probably the last message it will ever receive). The thought of a giant wounded bear who has already shown signs of aggression in the vicinity is not an attractive one to me.
Personally, I'd want something with a lot more oomph than the .243. No ambiguous messages. Lots of rifles that can provide much higher power without even going to the more unmanageable calibers, .375s, .416s, and the other shoulder-busters.
No bear spray. Give me an adequate firearm.