  Bing doubling is an operation which gives a satellite of a knot. It is also
applied to a link by specifying a component of the link. We give a formula to
compute the reduced colored Jones polynomial of a Bing double by using that of
the companion. This formula enables us to compute a lot of examples of the
reduced colored Jones polynomial of Bing doubles. Moreover, from this formula
we can derive a divisibility property of the unified Witten-Reshetikhin-Turaev
invariant of integral homology spheres obtained by \pm1 surgery along Bing
doubles of knots. This result is applied to the Witten-Reshetikhin-Turaev
invariant and the Ohtsuki series of these integral homology spheres.
