I voted 20% of the time.
I’m of the opinion that it best to use the Bismarck in SZ 111 with the hope that you can retreat it to SZ 112 with a damaged UK battleship left behind. But, if the UK player bids a UK fighter to Scotland to threaten a 2 plane scramble, I then will usually use it in SZ 110. I still send 2 subs to SZ 106.
With semi-experienced to very experienced players, I think the Axis lose the game because Russia gets too powerful (so I usually buy air/ground) if Germany isn’t very careful about their Sea Lion execution. Therefore, keeping the Battleship for G2 is important because it supports a viable Sea Lion threat. Having said that, I wouldn’t purposely not use it in SZ 110 or SZ 111 just to keep it.
I think safely pulling off Sea Lion is one of the most satisfying things to do when playing Germany. In a FEW games I’ve managed to do that WHILE (the most critical aspect), properly managing Russia. I’m not of the opinion that an Axis player, playing against a good Allies player SHOULD insist on executing Sea Lion by starting naval investments on G1. (I’m not a very good player period, but I think I understand the basics of the game). However, if you’re of the opinion that you need to buy boats G1 no matter what, then if not doing Sea Lion (because the UK purchases a lot for London), I think they need to be used for something other than just shucking infantry/artillery to Leningrad like maybe hitting Gibraltar on G2. Then you’re presenting a different credible threat to the UK (going after Cairo) and in theory have a chance.
Maybe 25% of the time the German battleship gets to retreat to SZ112 leaving behind that wounded UK battleship. Then if having won at SZ 106 and then on UK1 1-2 less units are placed on London than the standard 6 inf / 1 fighter, Sea Lion becomes a possibility. That I think is largely because the Bismarck is there for a bombardments (and less stuff required to mitigate a scramble to SZ110). This is the game where the Bismarck “replaces” the need to buy purchase a carrier G1; and hopefully a G1 ground/air purchase convinced Russia to not buy 3-4 tanks R1. If doing Sea Lion, I would then buy a carrier the round I hit London.