Curious what the minimum distance you will allow the White beast to approach you before opening fire? My wife and kids really want to see polar bears one day. (when I say approach you I mean a hungry bear actively stalking and moving towards you).
I'm thinking I'd feel best with a Lott.
The Lott works, a pal of mine has one, but I'd prefer the bottle neck profile of a .460 G&A (.458 Ultra) which feeds through a 602 action without modification. There is a trick I learned from the South Africans to get Lott performance out of a .458 Winchester cartridge in a Lott chamber, but I won't repeat it here. When I had my .375 Ultra built the original plan was for a .460 G&A, but then I had a Smith .375 barrel offered to me, and the rest is history.
For my purposes the .375 makes a better general purpose rifle that can be used for protection; if I can't do it with the .375, chances are I wouldn't be able to do it with the .460 either. I've developed a sense of comfort with this rifle, and in the event that I need a follow up shot, I could probably reacquire the target faster with the .375 than I could with a big case .458. and it carries much more authority than does my .44 beltgun. In a very close shooting situation, a hit to the CNS or to a big supporting bone with the 380 gr Rhino bullets at 2350 from the Ultra is pretty much a game changer. But if you shoot him in the chest at close range, chances are nothing handheld can stop him in time.
As to how close I let a bear approach depends on the bear, and the circumstances I'm faced with. If I'm guarding other people, I will never allow a bear to close to the extent I do when alone. I've been very close to some and haven't been overly concerned, while others scare me from a distance. Sometimes its something subtle that I can't really put my finger on, other times its overt. I would be very wary of a bear that was old and apparently starving. If you're a bear you don't want to scare me when I'm on foot. Polar bears tend to have a rather small personal space, in that you can crowd them far more than you can a grizzly before they react negatively, and this has provided me with hours of amusement. Once you do intrude in their personal space they will approach you, and that has resulted in some bear mortality when people are unprepared for it.
Early on I discovered that if a lone bear continues to close the distance with you after you have done all the standard stuff like yelling, jumping around, waving your arms, and shooting over their heads to no avail; running straight at them will often put the run on them. If you want an adrenalin dump, just try running at a half or three quarter ton bear! It works, as a rule. They tend to run off until they've had a chance to think things out. Now I don't recommend pushing your luck by keeping that up all day with the same bear, but it can get you out of trouble once, with a lone bear. Once the bear is moving away, it is in your best interest to do likewise. I wouldn't advise running at a female with cubs, although I know one guy who tried it, and was able to get inside a vehicle (just) before she got ahold of him. Females with cubs have little sense of humor and can put on truly frightening displays of ferocity. In any case, it is a poor tactic to employ in a multiple bear situation.
As to when I would shoot, I would certainly shoot to protect someone who was in danger, or when the running at them tactic doesn't work. If it doesn't work you have closed the distance from close, a matter of a few yards, to very close, a matter of feet; so you ought to have a plan "B" worked out and ready to go. I am more inclined to shoot when a bear's behavior scares me. This might be the guy who follows you at a distance for a long time, then as the daylight begins to fade he begins to circle you, spiraling closer with each pass. I don't like that much, particularly if I'm intending to sleep on the ground. The flat coastal areas don't provide much for natural protection from a bear. The only other time is when a bear has been raiding cabins and has become a danger, him I'll just dump on sight. But in those cases we know him, and picking out individual bears becomes easy after a while.