Fiber imaging bundles allow the transfer of optical images from place-to-place along narrow and flexible conduits. Traditionally used extensively in medical endoscopy, bundles are now finding new applications in endoscopic microscopy and other emerging techniques. PyFibreBundle is an open-source Python package for fast processing of images acquired through imaging bundles. This includes detection and removal of the fiber core pattern by filtering or interpolation, and application of background and flat-field corrections. It also allows images to be stitched together to create mosaics and resolution to be improved by combining multiple shifted images. This paper describes the technical implementation of PyFibreBundle and provides example results from three endomicroscopy imaging systems: color transmission, monochrome transmission, and confocal fluorescence. This allows various processing options to be compared quantitatively and qualitatively, and benchmarking demonstrates that PyFibreBundle can achieve state-of-the-art performance in an open-source package. The paper demonstrates core removal by interpolation and mosaicing at over 100 fps, real-time multi-frame resolution enhancement and the first demonstration of real-time endomicroscopy image processing, including core removal, on a Raspberry Pi single board computer. This demonstrates that PyFibreBundle is potentially a valuable tool for the development of low-cost, high-performance fiber bundle imaging systems.