For pt.I see Phys. Lett. A, vol.71, p.385 (1979). A recently developed non-perturbative iterative variational method has been applied to the bound polaron problem. The electron-phonon Hamiltonian is reduced in successive orders resulting in a transformed electronic Hamiltonian which gets an attractive phonon-induced potential from each order of reduction. The transformed electronic Hamiltonian has been solved numerically for a series of values of the parameters alpha , beta . Relation to perturbative solutions is discussed. Interesting localisation criteria derived from the calculated wavefunctions are also discussed.