  We suggest the so-called bosonic seesaw mechanism in the context of a
classically conformal $U(1)_{B-L}$ extension of the Standard Model with two
Higgs doublet fields. The $U(1)_{B-L}$ symmetry is radiatively broken via the
Coleman-Weinberg mechanism, which also generates the mass terms for the two
Higgs doublets through quartic Higgs couplings. Their masses are all positive
but, nevertheless, the electroweak symmetry breaking is realized by the bosonic
seesaw mechanism. Analyzing the renormalization group evolutions for all model
couplings, we find that a large hierarchy among the quartic Higgs couplings,
which is crucial for the bosonic seesaw mechanism to work, is dramatically
reduced toward high energies. Therefore, the bosonic seesaw is naturally
realized with only a mild hierarchy, if some fundamental theory, which provides
the origin of the classically conformal invariance, completes our model at some
high energy, for example, the Planck scale. We identify the regions of model
parameters which satisfy the perturbativity of the running couplings and the
electroweak vacuum stability as well as the naturalness of the electroweak
scale.
