In 1869, on suggestion from August Petermann, he joined an expedition to the Arctic Sea with the aim to investigate the islands of Spitsbergen and Novaya Zemlya and survey the ocean in their vicinity. Because of adverse ice conditions, only the first destination could be reached. During the course of the expedition, hydrographical measurements were performed and the climatological influence of the Gulf Stream on the eastern coast of Spitsbergen was demonstrated. After returning to his home country in 1870, he joined the German army as a surgeon in time for the Franco-Prussian war. For his military service he received a public commendation from the Grand Duke of Baden.
In 1871, Bessels joined the crew of American Arctic explorer C. F. Hall on the Polaris expedition as head of the scientific team. He and Hall soon came into conflict over control of the scientific research on the expedition. When Hall became ill in October 1871, Bessels remained by his bedside for several days, ostensibly in order to administer medical treatment. However, Hall suspected that Bessels was poisoning him, and consequently refused any further contact.
After Hall's death several weeks later, Bessels was among those who remained with the ship, the Polaris, when most of the crew became separated while trying to salvage supplies. Bessels and his party were eventually forced to abandon the ship, but were rescued and arrived back in the United States in 1873. Bessels and the other surviving members of the expedition crew were questioned by a naval board of inquiry about the events leading to Hall's death. The official conclusion was that Hall had died of natural causes and that Bessels had done his best in treating him. Nevertheless, following a forensic investigation in 1969 during which traces of arsenic were discovered on Hall's recovered body, today many scholars suspect that Bessels had in fact murdered Hall.
In the 1870s, Bessels stayed several years at the Smithsonian Institution in Washington, D.C., where he worked preparing the publication of the expedition's scientific results. The most important of these results was the proof that Greenland was an island, deduced from tidal observations and the discovery of walnut drift wood, indicating a connection between the Greenland Sea and the Bering Sea. The publication was planned for a total of three volumes, the first two of which were written by Bessels. However, only Volume 1, Physical Observations, was ever published, and this was later suppressed for errors and apparently never reissued
Bessels later considered mounting his own Arctic expedition, but eventually decided against it. He took part in another expedition to the northwest coast of America on the USS Saranac, but the voyage had to be interrupted after the ship was wrecked in Seymour Narrows, British Columbia. In 1878 Bessels published a book in German, Die amerikanische Nordpolexpedition, about the Polaris expedition. Bessels died of a stroke in the German city of Stuttgart at the age of 41.