Can I use the spectrophotometer to detect the quantitative amount of polymyxin B, given that it is colourless and the spectrophotometer requires colour change?
Yes, I guess you can, given that the compound contains a few peptide bonds and an aromatic ring, you should be able to quantitate the compound using absorption at 214 (which perhaps has high background), or 279 nm.
Or you can acquire an absorbance spectrum to find the wavelength with maximum absorbance that can be best used for quantitative experiments.