With the availability of large integral-field unit (IFU) spectral surveys of nearby galaxies, there is now the potential to extract spectral information from across the bulges and discs of galaxies in a systematic way. This information can address questions such as how these components built up with time, how galaxies evolve and whether their evolution depends on other properties of the galaxy such as its mass or environment. We present BUDDI, a new approach to fit the two-dimensional light profiles of galaxies as a function of wavelength to extract the spectral properties of these galaxies' discs and bulges. The fitting is carried out using GalfitM, a modified form of Galfit which can fit multi-waveband images simultaneously. The benefit of this technique over traditional multi-waveband fits is that the stellar populations of each component can be constrained using knowledge over the whole image and spectrum available. The decomposition has been developed using commissioning data from the SDSS-IV Mapping Nearby Galaxies at APO (MaNGA) survey with redshifts z 22 arcsec, but can be applied to any IFU data of a nearby galaxy with similar or better spatial resolution and coverage. We present an overview of the fitting process, the results from our tests, and we finish with example stellar population analyses of early-type galaxies from the MaNGA survey to give an indication of the scientific potential of applying bulge-disc decomposition to IFU data.