Long-lived particles (LLPs), particles with macroscopic lifetimes $\tau >10$~ps, appear in various extensions of the Standard Model (SM) that address fundamental questions like the particulate nature of dark matter or baryogenesis. The ANUBIS detector will achieve unprecedented sensitivity to such models compared to existing and approved experiments by instrumenting a large decay volume adjacent to the ATLAS experiment at the High-Luminosity LHC with tracking detectors. This paper outlines the proposed detector layouts for ANUBIS, explores their physics potential with a scalar LLP model, and identifies the preferred layout, comparing it to other experiments. The potential background contributions to ANUBIS are estimated using a data-driven method, and the topology of potential background events is studied using Monte Carlo simulations. Overall, ANUBIS is expected to probe branching ratios down to $𝒪$(10${}^{-6})$ for exotic decays of the Higgs boson to scalar long-lived particles with masses of 10, 15, 40, and 60 GeV and proper lifetimes of $c\tau =2.4,3.0,12$, and 18 m, respectively. Moreover, for branching ratios of 0.1% of the Higgs boson into long-lived scalars with a mass of 15 GeV, ANUBIS can probe a $c\tau$ range between $1.1\times {10}^{-1}$~m and $4.0\times {10}^3$~m.