Is it possible to reduce the spectral bandwidth to decrease the measurement time?

No, due to the employed Fourier-transform approach, there is no trade off between the working spectral range and the measurement time. Therefore, you cannot save time by reducing the spectral bandwidth of interest. In fact, the measurement time is affected by the spectral resolution that you want to achieve, i.e. the better the spectral resolution, the longer the scan of the interferometer and thus the measurement time.