What chance of seeing a polar bear in Svalbard?

My wife and I will spend 3 nights in Svalbard this June as part of our Scandinavian Arctic holiday. The highlight would be to see a polar bear, and it will be a big disappointment, especially for my Indonesian wife, if we don't.

Is there one particular guided trip from Longyearbyen, eg. horse ride, small boat, dogs, or whatever, that gives us the best chance of seeing a bear? I am well aware of how dangerous they are and that we should not leave town. We want to see a polar bear SAFELY. We will book at least 2 of the local tours there, one the 3 hour horseback and one other. I will probably book the tours this week and so would welcome an opinion about this first please.

Thanks in advance!

May 20 Flight HK - London
May 27 Flight London - Helsinki
May 29 Train/Bus Helsinki - Kemi - Tornio
May 30 Bus/Train Tornio - Kemi - Rovaniemi
May 31 Bus Rovaniemi - Inari
June 1-6 Car hire Ivalo - Kirkenes - Karasjok - Ivalo
June 6 Bus Inari - Nordkapp
June 9 Boat Nordkapp - Tromso
June 11 Flight Tromso - Longyearbyen
June 14 Flight Longyearbyen - Tromso
June 14-17 Undecided Tromso - ??? - London
June 18 Flight Depart London
June 19 Flight Arrive HK

I'm visiting Svalbard in July. From my reading, I believe that the likelihood of seeing a polar bear near Longyearbyen is pretty low. The best chance of seeing one is if you do a boat cruise that travels along the northern and eastern coasts of Svalbard, as the bears hang around the areas with more sea ice. Unfortunately, these trips are generally around 10 days long.

We want to see a polar bear SAFELY.

Check the advice here.
http://www.wildlifeextra.com/go/news/spitzbergen-bears.htm

A friend of mine went on a 10-day organised hike in the wilderness, and it was a disaster when they saw a polar bear. Unfortunately they now realised they had left the ammunition behind at one of the huts. Fortunately someone came by with a boat fairly soon, and they were able to radio them and arrange a retreat that way, but it meant cutting their hike short by a few days.

Basically we come to the conclusion that there are two ways to see a polar bear in reasonable safety
(1) staying on or close to a boat allowing rapid retreat by water
(2) being prepared to shoot it

Certainly there are 1-day boat trips available out of Longyearbyen, http://www.longyearbyen-camping.com/index_start.php?lang=en but no one mentions "polar bears" in relation to them, probably because the water near Longyearbyen is largely ice free in the summer, that there just aren't very many polar bears in that area in the summer. Otherwise, there wouldn't be an unfenced campsite at Longyearbyen, which can say that no polar bear has wandered into it in summer season at least 20 years.