By using a variant of the quantum inverse scattering method, commutation relations between all elements of the quantum monodromy matrix of the bosonic massive Thirring (BMT) model are obtained. Using those relations, the quantum integrability of BMT model is established and the S-matrix of two-body scattering between the corresponding quasiparticles has been obtained. It is observed that for some special values of the coupling constant, there exists an upper bound on the number of quasiparticles that can form a quantum-soliton state of the BMT model. We also calculate the binding energy for a N-soliton state of the quantum BMT model.