The May 2026 emergence of the rare Bundibugyo ebolavirus (BDBV) in northeastern Democratic Republic of the Congo (DRC) and its cross-border propagation into Uganda led to a Public Health Emergency of International Concern (PHEIC) declaration by the World Health Organization on May 17, 2026. The outbreak unfolds within a highly complex epidemiological and geopolitical landscape, characterized by active conflict, refugee displacement, and the absence of licensed vaccines or targeted therapeutics for this viral species. This paper presents an integrated, multi-scale operational and mathematical framework that couples zoonotic spillover dynamics and spatial human mobility across conflict-driven patches with a classical epidemiological compartmental structure (SEIHRD). By linking ecological surveillance (One Health) with bottom-up social mobilization, genomic sequencing, and humanitarian-access negotiation strategies, we derive a hybrid operational roadmap and evaluate it quantitatively. Using the exact spectral radius of the coupled next-generation matrix, we show that the two-patch system operates at a global basic reproduction number of R0 ≈ 1.20 under status-quo diagnostic and burial practices. Deploying the hybrid roadmap from Day 25 onward – scaling diagnostic-driven isolation and safe-and-dignified burial rates to their operationally attainable ceilings – drives the post-intervention reproduction number to R0 ≈ 0.69, placing the coupled system durably below the epidemic threshold. Full 90-day numerical integration of the twelve-state ordinary differential equation (ODE) system shows that this intervention reduces cumulative symptomatic cases by approximately 13% and cumulative deaths by approximately 16% relative to the unmitigated trajectory, with the reduction compounding over time as the post-intervention decay regime persists beyond the simulation horizon. We further perform a multi-parameter sensitivity and two-way interaction analysis, formalize diagnostic cost-effectiveness trade-offs under severe resource limitations, and conduct Bayesian parameter estimation via Metropolis–Hastings Markov Chain Monte Carlo (MCMC), obtaining Gelman–Rubin diagnostics R̂ < 1.01 for both estimated parameters. A fully self-contained, executable Python implementation is provided that exactly reproduces every quantitative result reported in this manuscript, together with an explicit falsifiability and experimental-validation roadmap.