Effective development of vibration energy harvesters is required to convert ambient kinetic energy into useful electrical energy as power supply for sensors, for example in structural health monitoring applications. Energy harvesting structures exhibiting bistable nonlinearities have previously been shown to generate large alternating current (AC) power when excited so as to undergo snap-through responses between stable equilibria. Yet, most microelectronics in sensors require rectified voltages and hence direct current (DC) power. While researchers have studied DC power generation from bistable energy harvesters subjected to harmonic excitations, there remain important questions as to the promise of such harvester platforms when the excitations are more realistic and include both harmonic and random components. To close this knowledge gap, this research computationally and experimentally studies the DC power delivery from bistable energy harvesters subjected to such realistic excitation combinations as those found in practice. Based on the results, it is found that the ability for bistable energy harvesters to generate peak DC power is significantly reduced by introducing sufficient amount of stochastic excitations into an otherwise harmonic input. On the other hand, the elimination of a low amplitude, coexistent response regime by way of the additive noise promotes power delivery if the device was not originally excited to snap-through. The outcomes of this research indicate the necessity for comprehensive studies about the sensitivities of DC power generation from bistable energy harvester to practical excitation scenarios prior to their optimal deployment in applications.