At 10:30 p.m. on May 26, 1941 a destroyer flotilla led by the already legendary Capt. Philip Vian appraoched the Bismarck. Comprised of four British Tribal-class DDs (Cossack, Sikh, Zulu and Maori) and the Polish-manned Piorun (British-made N-class DD), the flotilla would spend the night harassing the Bismarck with torpedo runs. About 20 torpedoes were fired altogether, but none hit. On the other hand, the Bismarck wasn't able to hit any of the attacking destroyers either.
This is probably due to Adm. Leutjens ill-advised order to keep the crew constantly at battle stations even when not under attack. Indeed, after the Battle of Denmark Strait, which was notable for very accurate German gunnery, the entire rest of the campaign was marked by very poor German shooting. None of the 24 Swordfish that attacked the Bismarck in two strikes was shot down. None of Vian's destroyers were hit. Neither the Prince of Wales nor the Sheffield were hit directly when the Bismarck fired at them. During the final battle on May 27 the Bismark one again scored no hits at all.