We present very high-energy optical photometry and spectroscopic observations of SN 2024bch in the nearby galaxy NGC 3206 (∼20 Mpc). We used gamma-ray observations performed with the first Large-Sized Telescope (LST-1) of the Cherenkov Telescope Array Observatory (CTAO) and optical observations with the Liverpool Telescope (LT) combined with data from public repositories to evaluate the general properties of the event and the progenitor star. No significant emission above the LST-1 energy threshold for this observation (∼100 GeV) was detected in the direction of SN 2024bch, and we computed an integral upper limit on the photon flux of F _γ (> 100 GeV)≤3.61 × 10 ⁻¹² cm ⁻² s ⁻¹ based on six nonconsecutive nights of observations with the LST-1, between 16 and 38 days after the explosion. Employing a general model for the gamma-ray flux emission, we found an upper limit on the mass-loss-rate to wind-velocity ratio of Ṁ / u _w  ≤ 10 ⁻⁴   M _⊙ / yr  s/km, although gamma-gamma absorption could potentially have skewed this estimation, effectively weakening our constraint. From spectro-photometric observations we found progenitor parameters of M _pr  = 11 – 20 M _⊙ and R _pr  = 531 ± 125 R _⊙ . Finally, using archival images from the Hubble Space Telescope, we constrained the luminosity of the progenitor star to log (L _pr / L _⊙ ) ≤ 4.82 and its effective temperature to T _pr  ≤ 4000 K. Our results suggest that SN 2024bch is a type IIn-L supernova that originated from a progenitor star consistent with a red supergiant. We show how the correct estimation of the mass-loss history of a supernova will play a major role in future multiwavelength observations.