Low-lying quadrupole shape dynamics is a typical manifestation of large-amplitude collective motion in finite nuclei. To describe the dynamics on a microscopic foundation, we have formulated a consistent scheme in which the Bohr collective Hamiltonian for the five-dimensional quadrupole shape variables is derived on the basis of the time-dependent Hartree-Fock-Bogoliubov theory. It enables us to incorporate the Thouless-Valatin effect on the shape inertial functions, which has been neglected in previous microscopic Bohr Hamiltonian approaches. Quantitative successes are illustrated for the low-lying spectra in Se-68, Mg30-34 and Cr58-64, which display shape-coexistence, shape-mixing and shape-transitional behavior.