We investigate the global $m=1$ bending mode instability in radially hot, Milky Way-like galactic discs using a linear perturbation framework. Our analysis shows that radial heating plays a key role in driving the instability: as the Toomre parameter $Q$ increases, the disc becomes progressively more susceptible to bending instability, accompanied by a systematic decrease in the growth timescale of the unstable $m=1$ mode. This behaviour reflects the enhanced in-plane random motions that weaken the effective restoring forces and facilitate the growth of bending modes. We further demonstrate that the dark matter halo significantly influences the stability properties of the disc, with low-mass halo systems supporting a larger number of unstable modes, while more massive halos enhance the vertical restoring force and suppress bending instabilities, leading to slower growth of the $m=1$ mode. Our results suggest that radially hot discs are inherently prone to global $m=1$ bending instabilities even in isolation, whereas massive dark matter halos act to stabilize the disc against such vertical distortions.
