We investigate the single-charmed baryonic decays ${\bar{B}}^0\to {\Lambda }_c^{+}\bar{p}$ and ${\bar{B}}^0\to {\bar{\Lambda }}_c^{-}p$, which receive contributions from both $W$-emission and $W$-exchange topologies, within the framework of perturbative QCD (PQCD). Higher-power corrections associated with the hadronic light-cone distribution amplitudes (LCDAs) of both the initial- and final-state hadrons are systematically taken into account. We find that these higher-twist contributions play an important role in baryonic $B$ decays and cannot be neglected. A sizable destructive interference between the $W$-emission and $W$-exchange amplitudes is observed, which significantly reduces the predicted branching fraction of ${\bar{B}}^0\to {\Lambda }_c^{+}\bar{p}$ and leads to improved agreement with experimental measurements. The doubly Cabibbo-suppressed decay ${\bar{B}}^0\to {\bar{\Lambda }}_c^{-}p$ is studied for the first time. Its branching fraction is predicted to be of order ${10}^{-8}$, placing it within the reach of future high-luminosity experiments. We further present the first theoretical predictions for the decay asymmetry parameters of both channels, which provide additional observables for testing the underlying decay dynamics and can be confronted with future experimental data.