Triangle A B C has a right angle at B, A B=1, and B C=2. The bisector of \angle B A C meets \overline{B C} at D. What is B D ?

**Answer Choices**

A. \dfrac{\sqrt{3}-1}{2}

B. \dfrac{\sqrt{5}-1}{2}

C. \dfrac{\sqrt{5}+1}{2}

D. \dfrac{\sqrt{6}+\sqrt{2}}{2}

E. 2 \sqrt{3}-1