BAHAMAS (BAyesian inference with HAmiltonian Montecarlo for Astrophysical Stochastic background) performs Bayesian inference of stochastic gravitational-wave background signals in simulated data for the Laser Interferometer Space Antenna. The code simulates frequency-domain data streams corresponding to the A and E time-delay interferometry channels and estimates source parameters using Hamiltonian Monte Carlo sampling implemented with NumPyro. It supports the analysis of stationary stochastic processes, such as power-law backgrounds, and can include overlapping sources and mission data gaps to evaluate their effects on signal reconstruction. BAHAMAS provides command-line tools for data generation, preprocessing, and parameter estimation from simulated or challenge datasets. The software produces parameter estimates and diagnostics for stochastic background models from full-resolution or coarse-grained frequency data.