The first ''happy time'' of 1940/41 was coming to an end in late spring 1941, as I say with the loss of three U-boat aces. There are not enough U-boats available for sustained mass attack on convoys. Convoy escorts were getting stronger. Luftwaffe air support? Yes, units were retained for Atlantic use and for sporadic bombing raids on Britain, but nothing like what would be required for sustained substantial air cover for Bismarck.
Keeping Bismarck in the Bay of Biscay is the worst option, as the British can keep tabs on the vessel far more easily than if she were in the Baltic or Norwegian waters. She can be kept under observation by French Resistance workers in the French ports, RAF reconnaissance and RN submarines operating in Biscay. And like Scharnhorst and Gneisenau, be on the receiving end of RAF bombing raids.
Now the four ships of Bismarck, Prinz Eugen, Scharnhorst and GneIsenau would be a substantial force operating together. On paper they could annihilate entire convoys and escorts. Indeed it might be argued that the U-boats could be made more effective by the Bismarck etc sinking large numbers of escort ships in defence of the convoys.
But the options for the British are not that grim. Firstly the Italian threat in the Med was waning, so Force H is available for Atlantic operations. Nelson and Rodney could provide convoy escorts, as protection against battleship attack. The Home Fleet would not need to be constantly at sea, until the German force cleared Biscay into the open Atlantic. The longer the Germans delay, the more time POW has to work up into something more efficient than at DS, so a combination of fast battleships as well as battlecruisers are available. And as I say the weak point in German logistics are four fuel hungry ships - with German supply tankers just waiting to be found and sunk in the open Atlantic by RN cruisers.
The longer the Germans delay the more unfavourable it becomes for them, especially once Barbarossa is under way. And Churchill would have one other nice trick under his sleeve, if the Germans did come out. He would want American warships in the Atlantic, close to convoys etc so that the Germans could end up firing on an American ship by mistake......
Tirpitz? Well by early 1942 the fuel situation was becoming more critical for the Germans, and the USA is now in the war. But Hitler has too many fronts to fight on, too many enemies.....
''Give me a Ping and one Ping only'' - Sean Connery.