I believe that few, if any, WW2 battleships were sunk by bombs alone, with the exception of the Roma which was hit by the huge radio-controlled FX-1400 bombs, and of course the stationary Tirpitz, capsized by enormous "earthquake" bombs.

As has already been pointed out, to sink a ship you need to let the water in, and that means making big holes in the hull below water level. That's exactly what torpedoes are designed to do, but I don't believe that dive-bombers were capable of carrying bombs heavy enough to inflict this on a well-protected modern battleship. They could make one heck of a mess of such a ship, but were unlikely to sink it.

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Tony Williams: Military gun and ammunition website