On May 18, 1941 the Bismark and heavy cruiser Prinz Eugen attempted to break out of the North Sea into the Atlantic. They were spotted and reported to the British who assembled a sizable force to intercept them. On May 24, after having been shadowed by a smaller British ships, the heavy cruisers Suffolk and Norfolk, the Bismark and Prinz Eugen were sought out and engaged by the British in the form of the battleship HMS Prince of Wales and the battlecruiser HMS Hood along with a destroyer escort. Their destroyer escort proved almost useless in aiding the Brits because of extremely rough seas. In addition, the two cruisers, that had been shadowing the Germans, had temporarily lost contact with the German battleships and were now far from the battle. The Hood opened fire on the Prinz Eugen, at about 0552 hours, mistakenly with the belief that it was the Bismark. Shortly thereafter it engaged the Bismark. At 0600 the Bismark fired a salvo at the Hood and a 15 inch shell fired from a distance of 9 miles (get that - 9 miles) hit the Hood and apparently ignited one of her magazines. It caused a huge explosion and parts of the Hood rained down on another British ship about 1/2 mile away. The Hood actually broke in two and sank about 3 minutes after being hit, she took with her 1,415 men, including Vice-Admiral Holland who was the commander of the British attack forces. Then the Prinz Eugen and the Bismark targeted the Prince of Wales and that ship was fairly to heavily damaged before it turned and retreated under cover of a smoke screen. After news of this attack reached British Prime Minister Winston Churchill, he gave the order: "Sink the Bismark". As the HMS Hood was one of the prides of, if not the pride of, the British navy, this resulted in the great majority of England's available naval and air forces searching out the Bismark.
Bismark and Prinz Eugen were also damaged in the battle of The Denmark Strait. The Bismark taking some pretty hard hits, one resulting in a serious leak of fuel. When the Captain of the Bismark, Ernst Lindemann, requested permission from Admiral Gunther Lutjens to pursue and destroy the Prince of Wales, Lutjens denied it. After a repeated stronger request, Lutjens again denied it apparently following orders to avoid unnecessary contact with warships and risk of damage in order to fulfill Bismark's intended mission of hunting down and destroying enemy merchant ships. What happened though was not that. Instead, the Bismark turned toward Brest, France for sanctuary because of the fuel leak, it was a serious one. She was shadowed by the two British cruisers and the damaged prince of Wales. The Prinz Eugen, not badly damaged, was then ordered to continue on its hunt for merchant ships and the Bismark, at about 1830 that night turned on the British ships allowing the Prinz Eugen to slip away. Later that night, at about 2200 hours, HMS Victorious (an aircraft carrier) sent several Fairey Swordfish torpedo bombers at Bismark. They engaged her but did little damage with only one torpedo hitting the Bismark in its heavy armor. The Brits, both their ships and aircraft lost contact with Bismark but it was regained on May 26 and Bismark was still too far off for Luftwaffe cover. HMS Ark Royal now took over and launched an attack on the Bismark that was almost catastrophic for the Brits in that the planes attacked one of their own ships. Luckily they missed with many torpedoes and the others failed, exploding prematurely, due to unreliable detonators. Ark Royal soon launched another attack on Bismark in terrible weather and this time the torpedoes were equipped with much more reliable detonators. Two or three torpedoes found their mark and a critical hit was registered on the steering mechanisms of the Bismark.
With her steering out she was not maneuverable. The British took advantage of this on May 27 and attacked Bismark with battleships HMS Rodney and HMS King George V. They inflicted heavy damage causing Bismark to list severely but the Bismark did not sink. The British battleships, low on fuel, retreated and the HMS Doretshire, a heavy cruiser, then attacked with torpedoes. Despite three torpedo hits, the Bismark still did not sink but did sustain very heavy casualties. At 1040 hours, in an irony of ironies, the Germans scuttled the Bismark and she sank. Only 111 German sailors were rescued by the British who soon fled the area upon receiving reports of U-Boats operating nearby. One of those survivors died of his wounds while on the British ship. A German U-boat later rescued 3 more and another German ship later rescued 2 more. There were, in total, only 115 survivors; in all 2,085 of Bismark's crew perished. Churchill was very pleased with this result but I would guess that he never, not for even a moment, thought it would be the Germans who would be the ones to follow his order to "Sink The Bismark".
The above post heavily relied on the Wikipedia article about Operation Rheinübung.
To read an interview with a survivor of the Bismark, click on this link:
All the best,