How far can they swim and for how long can they hold their breath?

Polar bears can swim steadily for many hours in order to get from one piece of ice to another. They have water-repellent coat and partially webbed feet, which both are adaptations to swimming. Although known individual bears have only been recorded swimming about 100 km (1km = .621 miles) or so, they are likely capable of swimming much further if necessary. However, this kind of effort is very expensive in terms of energy, so swimming such long distances is likely not done frequently. The longest a polar bear in the wild has been timed holding its breath while diving is 72 seconds. 

according to  http://pbsg.npolar.no/pb_faq.htm

Others say polar bears can swim hundreds of miles if they want to. They kinda just float and paddle as they see fit. They politicos use a polar bear hopelessly stuck on polar ice poster to suck you into their brand of emotional group think.