Multimodal interference is frequently pointed out as one of the main limiting factors in gas sensing setups which utilize hollow-core optical fibers as gas cells. In this paper we demonstrate suppression of optical fringes that originate from propagation of higher order modes in an anti-resonant hollow-core fiber by controlled fiber bending. Near-infrared broadband absorption spectroscopy is used to characterize the fringe patterns observed when higher order modes are excited and suppressed. A tunable laser diode emitting near 1687 nm is used to present positive impact of bending the hollow-core fiber on signals recorded with both direct absorption spectroscopy and wavelength modulation spectroscopy of methane. Bending radius of 30 mm was found optimal for the setup presented in this work, leading to sub-ppm-level detection limit at 1687 nm with 7.35-m-long fiber.