By using a photonic bandgap (PBG) fiber bundle and a monochrome CCD camera, we experimentally demonstrate an all-fiber spectrometer. A total of 100 Bragg fibers that have complementary and overlapping bandgaps are chosen to compose the fiber bundle. A monochrome CCD is then used to capture the binned image. To reconstruct the test spectrum from a single CCD image, we develop an algorithm based on pseudoinversion of the spectrometer transmission matrix. We demonstrate that the peak center wavelength can always be reconstructed within several percent of its true value regardless of the peak width or position, and that, although the widths of the individual Bragg fiber bandgaps are quite large (60-180nm), the spectroscopic system has a resolution limit of approximately 30nm. Moreover, we conclude that, by minimizing system errors, the resolution can be further improved down to several nanometers in width. Finally, we report fabrication of PBG fiber bundles containing hundreds of fibers using a two-stage drawing technique. This method constitutes a very promising approach toward industrial-strength fabrication of all-fiber spectrometers.