Last year I circumnavigated Svalbard on the Academik Sergei Vavilov. We travelled beyond 80 deg N and saw the polar ice cap. It was a great trip and later this year we will visit the Antarctic on its sister, the Ioffe. The ship is a Russian scientific research vessel with a very high ice rating, which means it can handle situations that most other ships on this route could not. It also has a sophisticated stabilisation system (designed to facilitate accurate scientific measurements - and perhaps tracking NATO submarines?) which we did not need as the sea was so calm. Generally we were very lucky with the weather.
The ship carries no more than 100 passengers. This was quite a good number, as it meant that it was big enough to handle rough weather (which we did not have) and we could get to know a variety of people. It was not so big that it felt like a city on the sea.
We saw four polar bears, but while there is a good chance of seeing them, you are very unlikely to get close. Even when a bear was on the shore (and especially when it was swimming), our zodiacs kept well away, both for safety and to avoid stressing the bear.
I do not think that it is at all necessary for a competent photographer to go on a specific photography tour for such a trip. The crew and expedition leaders (the latter were from a variety of countries) did their best to give everyone a great experience, depending on their needs. Almost every day we went out in zodiacs twice a day, sometimes staying on the water and sometimes on land. When on land different options were made available, depending on what people wanted to do. I usually went with the slow group, because that gave lots of time for photography. Usually we were on land for two to three hours at a time, and that is really enough.
The voyage had an official photographer, Nikon Ambassador Daisy Gilardini
http://www.daisygilardini.com/#/0 and I spent a lot of time with her - it is always interesting to be around an expert. But even if she had not been there (not every voyage has an official photographer) I would still have had far more photo opportunities than I could exploit.
Most of the other expedition leaders had MAs or PhDs in relevant subjects. Some had written books. There were lots of lectures on the Arctic and its history and I went to as many of those as I could. The expedition leaders were very professional and greatly added to the experience.
The company tries to offer sharing arrangements for single travellers, and that can help to keep control over the cost. There were several singles who shared in this way.
We also spent a day and half in Longyearbyen, the capital of Svalbard, and that was as much time as I would want to spend there. We did take the opportunity to go dog sledding (including harnessing the dogs to the wheeled sledges (no snow in Longyearbyen in the summer). It was a lot of fun. I would not recommend basing yourself in Longyearbyen. We met a Danish couple who had done that and it did not sound very appealing.
Here is a link to some of my photos of the trip.
http://anthonymac.smugmug.com/Travel/Svalbard-July-2014/