We present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for the special orthogonal group SO(2k + 1). This bijection is motivated by the direct-sum-decomposition of the rth tensor power of the defining representation of SO(2k + 1). To formulate it, we use Kwon's orthogonal Littlewood-Richardson tableaux and introduce new alternative tableaux they are in bijection with.Moreover we use a suitably defined descent set for vacillating tableaux to determine the quasi-symmetric expansion of the Frobenius characters of the isotypic components.