Bismarck was no different to other BBs in being close to impossible to sink with gunfire - though I've seen one report of the damage which suggests that she had nevertheless been left in a sinking condition before being scuttled/torpedoed. (That is, she had holes below the waterline in her citadel and would eventually sink.)
Bismarck's armour belt was built with a prominent socalled turtle deck. A heavy sloped plate behind the main belt. This meant that even if shells penetrated the main belt they would be unlikely to go beyond the sloped plate and into the internals of the ship. This was common practice in early 20th century (Hood had a similar, but not as heavy system) and was especially effective at short to medium range, where the shell trajectory would be flat. And long range, which became a real possibility in late WWI, a plunging shell could however penetrate the main deck without ever meeting the main belt or the turtle deck. Bismarck was the only modern battleship built with the turtledeck protection system so prominent, and has often been acused of just being a "dusted off WWI design".
Hood's armour arrangement was similar and at ranges shorter than the OTL would have had a very good chance of defeating Bismarck's shells, but at exactly the range and inclination met in OTL a shell could go through the relatively thin upper belt and almost perpendicularly through the turtle deck.
When Bismarck met KGV and Rodney the fighting was at relatively short range meaning a lot of hits very quickly reducing Bismarck to a floating wreck, but it is likely that no shell made it to the machinery or magazines. If she actually sank because of the scuttling charges, the torpedoes or damage recieved from the gunnery is IMHO rather irrelevant as she long before that had been reduced to a wreck not capable of fighting back.
Modern capital ships were relatively difficult to sink with gunfire alone (short of a magazine explosion), but Bismarck especially so. The discussion anyway is mainly theoretical, as we have very few instances of modern battleships being exposed to substantial gunfire. They probably all were quite vulnerable to their fighting capacity. Just take South dakoto who was effectively blinded after being hit with a few 14" and a lot of lighter shells.