I like to think that the story behind is that Prinz was invited by Sheffield (who she has begun dating; see post #4834292) to a Christmas party at the shipgirl base, and asked Bismarck to join her. Bismarck, however, doesn't want to go to party as she finds the British shipgirls annoying, but begrudgingly accepts anyway because she doesn't want to spoil Prinz's evening.
At the party, Prinz goes off to join Sheffield, and Bismarck goes and finds a quiet place to sit at. To her horror, she bumps into Ark and Warspite and immediately strike up a conversion with her which goes on for hours, much to the German's dismay. Not wanting to be stuck with them, Bismarck concocts a plan to get rid of them: first she'll get them to drink an excessive amount of alcohol and then make her escape when they get drunk. The plan backfires, however; Whilst the first part goes as planned, Bismarck overestimated her tolerance level and becomes drunk herself, with the three of them getting on stage together and singing karaoke.
The night ends with both Prinz and Sheffield saying their goodbyes and carrying their drunken comrades back to their quarters.