When the Bismarck and the Prinz Eugone broke out into the Atlantic, Hood and Prince of Wales were sent to pursue. This led to the Battle of the Denmark Straits in which Hood was sunk, Prince of Wales damaged, failing to sink the Bismarck but at least causing enough damage to abort it's sortie and sail for French Atlantic ports.
I cannot understand why the Royal Navy would send Hood, which was badly in need to modernization, being largely neglected in the inter war years, and Prince of Wales which was brand-new, suffering major teething issues which would cripple it in battle.
Alternatively, more capable ships like HMS Nelson, HMS Rodney, HMS Warspite could have been dispatched or maybe even HMS King George V which was at least a little newer than P of W. Where these ships available or tied up else ware? Would these ships have fared any better in battle with the Bismarck?
For the most part, it was because they were the ships available to cover the region that Bismarck happened to go through. Of the ships you name, Nelson and the carrier Eagle were in the South Atlantic, having left St Helena for Freetown on the same day Bismarck sailed from Poland to Norway. Warspite and the remainder of the Queen Elizabeth class were in the Mediterranean, operating around Crete. On the same day that Hood and Prince of Wales sailed to the Denmark Strait, Rodney was setting off for a refit in the USA, in companion with the troopship Britannic. King George V, Repulse, and the carrier Victorious were also hunting for Bismarck. However, instead of covering the Denmark Strait, as PoW and Hood were, they were covering the other exit to the Norwegian Sea, between Iceland and the Faroe Islands. This was a much greater distance to cover, and more vital, as an escape through this exit would put Bismarck and Prinz Eugen closer to the convoy routes.
I'd also point out that Hood and Prince of Wales weren't necessarily doomed to fail against Bismarck. On paper they outgunned her severely. If Holland hadn't chosen to make an approach that masked his after turrets, he could have made this firepower advantage tell. If a lucky hit hadn't caused Hood to explode, he might still have had that chance.