How to difference a loud sound (playing notes), from a soft noise in spectrum. (Pitch detection with bass)
The intuitive answer is to threshold with respect to the magnitude. 

You are performing a short-time Fourier transform (STFT), that is, segmenting the original into short time windows and performing Fourier transform on each of them. The output of STFT is a frequency-time (t-f) bin table of complex values. 

There is an inherent tradeoff in STFT. The shorter your windows are the higher is your time resolution and the lower is your frequency resolution. If you want a high-frequency resolution you will have to use longer windows at the cost of poor time resolution. This paper gives a clue on window length optimization. otherwise, you can simply use the common music window length from papers or online examples. For bass, the frequencies are low = long wavelength, hence, you will want longer windows. 

Basically, you can get the magnitude and\or the angle of your t-f table. Assuming your bass has much more energy than the noise gathered by the system, you can look at the magnitude of bins in the required frequency range and drop time segments below a certain threshold. Play a bit with the result and present it as an image. It will give you a science of where to cut. This is a MATLAB example of presenting the magnitude as an image (also called spectrogram)