So we actually get to see how Prinz's Bismarck-neesama looks in Yua's art style.
... Now I hope to see her try to invade the Yokosuka base in an attempt to save Prinz from what is "obviously" a den of depraved corruption and insanity.
During their brief time together, Prinz Eugen was ultimately able to escape because the Bismarck single handedly engaged a group of British warships, mostly cruisers if I'm not mistaken. Bismarck made a good account of herself, suffering virtually no damage, and breaking off cleanly to make her own escape.
So yes, there's more than enough reason to justify the relationship they have. Bismarck would be something of a hero to Eugen, who is a bit of a hero in her own right when you get down to it.