The resistivity \ensuremath{\rho} and thermoelectric power S of the doped Kondo semiconductor (${\mathrm{Ce}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{La}}_{\mathit{x}}$${)}_{3}$${\mathrm{Bi}}_{4}$${\mathrm{Pt}}_{3}$ are examined to determine the effects of doping on the narrow gap exhibited by this compound. The transport data provide evidence that the energy gap progressively disappears with increasing concentration of La. The T=0 transport-energy gap, as determined from either \ensuremath{\rho} or S, scales with the single-impurity Kondo energy scale ${\mathit{T}}_{\mathit{K}}$, as estimated from magnetic-susceptibility measurements, independently of x for x\ensuremath{\le}0.25. This result suggests that the gap arises from band hybridization that is driven by Kondo-like correlations rather than from single-electronic interactions.