Li2RuO3 with a honeycomb structure undergoes a drastic transition from a regular honeycomb lattice with the C2/m space group to a valence-bond solid state of the P2(1)/m space group with an extremely strong dimerization at 550 K. We synthesized Li2Ru1-xMnxO3 with a full solid solution and investigated doping effects on the valence-bond solid state as a function of Mn content. The valence-bond solid state is found to be stable up to x = 0.2, based on our extensive experiments: structural studies, resistivity, and magnetic susceptibility. On the other hand, the extended x-ray absorption fine-structure analyses show that the dimer local structure remains robust even above x = 0.2 with a minimal effect on the dimer bond length. This indicates that the locally disordered dimer structure survives well into the Mn-rich phase even though the thermodynamically stable average structure has the C2/m space group. Our results prove that the dimer formation in Li2RuO3 is predominantly a local phenomenon driven by the formation of orbitally assisted metal-metal bonds and that these dimers are relatively robust against doping-induced disorder.