In principle, it's no different from measuring the bandwidth of any receiver. You need to produce a modulated signal from a test source and then see what your detector (demodulator) gives you. The wider the bandwidth of the receiver, the more data or the faster the analogue signal it can detect. (Is that what you had in mind for your question - sorry if it's talking down but it's hard to assess your initial level of knowledge.
An obvious (?) way would be to amplitude modulate light of a suitable wavelength and see how the shape of the modulating signal waveform is affected - e.g. look for the effect on a very fast pulse. Alternatively, use a swept frequency for modulation and see the amplitude of the signal that your detector demodulates at different modulating frequencies.
Btw, thw signal bandwidth is distinct from the "spectral bandwidth" which is the range of wavelengths that the detector can actually detect - see the spec sheet in the link.