We present laser-based methane detection near 1651 nm inside an antiresonant hollow-core fiber (HCF) using photothermal spectroscopy (PTS). A bismuth-doped fiber amplifier capable of delivering up to more than 160 mW at 1651 nm is used to boost the PTS signal amplitude. The design of the system is described, and the impact of various experimental parameters (such as pump source modulation frequency, modulation amplitude, and optical power) on signal amplitude and signal-to-noise ratio is analyzed. Comparison with similar PTS/HCF-based systems is presented. With 1.3 m long HCF and a fiber amplifier for signal enhancement, this technique is capable of detecting methane at single parts-per-million levels, which makes this robust in-fiber sensing approach promising also for industrial applications such as, e.g., natural gas leak detection.