We describe a magnetic bottle time-of-flight electron spectrometer designed for time-resolved photoemission spectroscopy of a liquid microjet using extreme UV and X-ray radiation. The spectrometer can be easily reconfigured depending on experimental requirements and the energy range of interest. To improve the energy resolution at high electron kinetic energy, a retarding potential can be applied either via a stack of electrodes or retarding mesh grids, and a flight-tube extension can be attached to increase the flight time. A gated electron detector was developed to reject intense parasitic signal from light scattered off the surface of the cylindrically shaped liquid microjet. This detector features a two-stage multiplication with a microchannel plate plus a fast-response scintillator followed by an image-intensified photon detector. The performance of the spectrometer was tested at SPring-8 and SACLA, and time-resolved photoelectron spectra were measured for an ultrafast charge transfer to solvent reaction in an aqueous NaI solution with a 200 nm UV pump pulses from a table-top ultrafast laser and the 5.5 keV hard X-ray probe pulses from SACLA.