  A class of $\mathfrak{o}_{2n+1}$-invariant quantum integrable models is
investigated in the framework of algebraic Bethe ansatz method. A construction
of the $\mathfrak{o}_{2n+1}$-invariant Bethe vector is proposed in terms of the
Drinfeld currents for the double of Yangian $\mathcal{D}Y(\mathfrak{o}_{2n +
1})$. Action of the monodromy matrix entries onto off-shell Bethe vectors for
these models is calculated. Recursion relations for these vectors were
obtained. The action formulas can be used to investigate structure of the
scalar products of Bethe vectors in $\mathfrak{o}_{2n+1}$-invariant models.
