The effect of bootstrap current perturbation on the onset of neoclassical tearing modes (NTMs) is studied numerically based on two-fluid equations, using externally applied resonant magnetic perturbations (RMPs) as triggers. With increasing the bootstrap current density, a larger RMP is found to be required to excite the NTM's onset when the bi-normal electron fluid velocity is in the ion drift direction, being contrary to the conventional understanding that the bootstrap current perturbation is always destabilizing. For the electron fluid velocity in the electron drift direction, however, the opposite results are found.