As we all know, the Battleship Bismarck of the german navy was the most promising part of the german navy. Or was it? Germany had been building an air craft carrier in 1938, and she could have been ready by 1941. What if she, the Graf Zeppelin, was completed and was sent along with the Bismarck and Prinz Eugen on operation rhine. The Bismarck could crush any escorts, including a battleship to a convoy, and the Zeppelin could provide air cover and again crush a battleship, and the Prinz Eugen could attack the merchant ships with impunity.
If the Hood and Prince of Wales found them, then it is more then likely they would receive little, if any damage, as the aircraft from Zeppelin could destroy them before they even got in range. They could then wipe out as many convoys as they chose, and eventually head either to occupied france or norway to get repairs. They could then go out and join Scharnhorst and Gneisenau and then when Tirpitz is ready, they could all join in one great fleet. Such a fleet, with the Bismarck, Tirpitz, Scharnhorst, Gneisenau, Graf Zeppelin, and Prinz Eugen could simply attack any convoy they chose, and the British might need all of its carriers and Battleships to attack them, and if they survived into december, with the pacific war beginning, then the British would have to divide their navy for the pacific and atlantic wars.
I personally think that the US would have come in, then we are looking at a battle on the scale of Jutland or Leyte, as Iowa was sent to counter Tirpitz in 1943, then they would probably have to send another 2 battleships and a carrier to counter that force. If they met, then it would be one hell of a battle.