Den Norske Los, Vol. 7, available online, published in both Norwegian and English, has a separate chapter on Jan Mayen, in which the coastline is described in considerable detail. Note that this volume has not been updated since 2018 and so does not deal with the Nature Reserve limitations.
Challenges
There are no SAR facilities on Jan Mayen and it is outside of helicopter range, so you are on your own when visiting there.
Only very experienced sailors with a sturdy offshore boat should attempt the passage to Jan Mayen.
The weather is unpredictable and potentially severe, the presence of Beerenburg can cause unpredictable and violent katabatic winds, and you will have to deal with the fact that there are no sheltered all-weather anchorages. Though some shelter can be found on the lee side of the island, even in moderate weather you can expect to find surf on the beach.
As the sea temperature is low, wearing survival suits and carrying equipment in fully waterproof bags is advisable for the dinghy ride to shore.
Although in clear weather Beerenberg can be seen from a great distance, it is often obscured by mist or rain. Fog is present as much as 20% of the time in the summer months.
Ice
The ice-free season at Jan Mayen usually occurs between June and November, except when the polar storis (multi-year) pack ice drifts out from east Greenland, keeping its waters clogged with ice until much later in the spring.
Based on this, sailing there before late June or early July when, as long as the sea temperature remains above 3°C, you are unlikely to see any new ice forming, is not recommended.
Jan Mayen does have several tidewater glaciers but we are not aware that berg ice causes any problems with anchoring or navigation in the area.
Isbjørner (Polar Bears)
Polar bears are only found on Jan Mayen in the winter.
Chartering
Seil Norge organizes skippered sails to Jan Mayen, with a focus on climbing Beerenberg, leaving from and returning to Svalbard.