Traditionally, there's not a great variety of options for seeing these magnificent creatures (and if things carry on as they are, there'll be even fewer fairly soon, some would say). And the fact remains that if you're going to do, it's going to cost you. A lot. But there's one or two special options about for making the most of the opportunity.
There are really two places where the bears come close enough to civilisation to be accessible to you and me. One is Spitsbergen, off the very far northern coast of Norway, for which the best season is summer when the bears are foraging for food; the other Churchill, in the remote north of Canada, where they gather in huge numbers in October and November each year.
The default option for this sort of thing is a cruise, which is great, but really expensive. A 6-day Spitsbergen cruise in the lowest available class of cabin starts at £1195 with Hurtigruten, based on two sharing, and that's only once you've got to Longyearbyen, which isn't the cheapest place in the world to reach... Hurtigruten's Spitsbergen cruises are the cheapest we've found of the sort, and they've good, if not outstanding, environmental credentials.
One better is to travel round Spitsbergen under your own power. Hurtigruten offer two trips of this sort - a 9-day kayaking trip (covering much the same territory as the 6-day cruise) at £1365, or a 13-day trekking holiday costing £1755. These trips both sound incredible, though the idea of going on polar bear watch during the night while your fellow holidaymakers snooze in their tents around you is mildly unnerving!
Getting to Spitsbergen - Hurtigruten will book it for you if you ask them to, quoting a price of £670 return at the moment (including offsetting), which includes an overnight in Oslo. The most environmentally friendly way we could find takes you from Newcastle to Bergen by overnight ferry (from £43 return, and offering a chance to take in the fjordlands on your way), followed by a flight from there which will cost about £250 with SAS, though will involve changing planes in Tromso.
Perhaps the ultimate polar bear greenhike, though, actually takes you to North America. This isn't something we'd normally go in for, but then, there aren't any other places where you've actually got the opportunity to help study the environment at the same time as having a dream encounter with polar bears.
Earthwatch have an expedition in October from Churchill which they call 'Climate Change at the Arctic's Edge'. You spend 11 days staying at the Churchill Northern Studies Centre, helping scientists from the University of Alberta monitor ecosystem responses to global warming - in the middle of the highest concentration of polar bears in the world. Once in Churchill, the trip comes in at £1395, though it should be said this is a true 'offset yourself' trip - you will be working!
Again, it's getting to Churchill that spirals the cost, and of course the environmental impact. Flying there from London will cost something in the region of £800. But again there is an incremental improvement you can make, and boost the scope of your trip at the same time. Fly to Toronto, which costs from £250 return, then take the train up to Churchill via Winnipeg. This will take you through some of the most spectacular scenery in the world, and cost in the region of £250 return. That saves you £300, which could happily fund a few days looking around Toronto and Winnipeg on the way.