Why Hood closed rapidly on Bismarck

Did Hood approach Bismarck bow-on because her armor could not withstand the engagement, or because she needed to close the range?

The primary purpose was to close the range.

Hood's bow-on approach was intended chiefly to close the range. That course limited the number of British guns that could fire during the initial approach. It also reduced the time spent at the longer range from which the action began. Rapid range reduction was the dominant motive rather than a detailed claim about the geometry of Hood's armor.