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In quantum walks, the spread velocity of dimer-monomer bound state is determined by the maximal group velocity of their energy band, which is much smaller than that in the single-particle case. 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While dimer-monomer bound states are manifested as a single particle attached to a dimer bound pair, it is still unclear about quantum walks and Bloch oscillations of dimer-monomer bound states. Here, we revisit three-particle bound states in the Bose-Hubbard model and find that interaction-induced impurities adjacent to bound pair and boundaries cause two kinds of bound states: one is dimer-monomer bound state and the other is bound edge state. 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