The paper describes a time-resolved photoemission (TRPES) apparatus equipped with a Yb-doped fiber laser system delivering 1.2-eV pump and 5.9-eV probe pulses at the repetition rate of 95 MHz. Time and energy resolutions are 11.3 meV and ~310 fs, respectively; the latter is estimated by performing TRPES on a highly oriented pyrolytic graphite (HOPG). The high repetition rate is suited for achieving high signal-to-noise ratio in TRPES spectra, thereby facilitating investigations of ultrafast electronic dynamics in the low pump fluence (p) region. TRPES of polycrystalline bismuth (Bi) at p as low as 30 nJ/mm2 is demonstrated. The laser source is compact and is docked to an existing TRPES apparatus based on a 250-kHz Ti:sapphire laser system. The 95-MHz system is less prone to space-charge broadening effects compared to the 250-kHz system, which we explicitly show in a systematic probe-power dependency of the Fermi cutoff of polycrystalline gold. We also describe that the TRPES response of an oriented Bi(111)/HOPG sample is useful for fine-tuning the spatial overlap of the pump and probe beams even when p is as low as 30 nJ/mm2.