I ought to start by pointing out that the Germans insist that they scuttled the ship. The Brits would make the point that two high-explosive torpedoes from "The Dorsetshire" probably didn't help to keep it afloat.
The Brits needed a "win" (and as someone else said, revenge.)
The Royal Navy surface fleet was 7 times the size of the German Navy, ultimately, the Bismarck would eventually have lost a battle, and whereas the British could afford to lose a boat or two, the Germans just couldn't. Hence, most of their navy stayed away from front-line action after that. That was probably not an unintended consequence.
We'd lost "The Hood", which contrary to one of the other answers was not (by any means) our finest ship. She was the biggest, but she was undergunned, a bit slow and disliked by all who sailed in her. Extensive long-term (and actually unfinished) modifications had made her a "bitza".
It was "old technology" 170mph biplanes that first crippled the Bismarck. But ultimately force of numbers ensured her fate.