We investigated the low speed bearing fault diagnosis under bounded noise background in three typical conditions. These situations included when the frequency of bounded noise was much larger, a little larger, and a little smaller than the driving frequency. Through the investigation of a harmonic signal in these three situations, we found the effect of stochastic resonance method was the best in the first situation, while it was invalid in the third situation. For the third situation, we introduced the vibrational resonance method by adding an auxiliary signal to extract the character frequency successfully. Then we also studied the low speed experimental bearing fault signal under bounded noise background, and it showed the same results as those of the simulation harmonic signal case. The methods and results of this paper might be useful in practical engineering, especially in extracting the weak character signal in the bounded noise background.