The Bismarck AAA armament was unusually bad even among the other BBs designed at the same time as she was; largely a result of it being a dusted-off WWI design.
Anyway, main point is the steady diet of crappy History Channel "Nazi Superweapon" documentaries has obscured over time what a horrible design Bismarck was.
Yamato sort of has the same problem.
AA was afterthought in early WWII even with the Yamato. (Had no logical or cohesive FC system)The US designs which came out the Iowa class with radar control were the best that anyone put out.
Actually, the Bismark AAA defenses were quite good for it's time...The problem was the athe fire control systemn could not adjust hit slower moving targets, like British Swordfish torpedo bombers, which could make 60 mph on a good day with a torpedo slung and a tailwind.
OTOH, she did beat the Hood & Prince of Wales single-handed.
In my opinion, the American ships built around 1935 or thereafter (or significantly rebuilt) were the only ones that had substantial AAA. And even then, the ships had to be numerous and tightly-grouped to provide effective fire, unless you're talking about the Iowa-class and the Massachusetts-class battleships or the Essex-class carriers.
Otherwise, a large number of aircraft could still be overwhelming. The best defense against incoming bombers has always been fighter aircraft.