When tidal waves enter a funnel-shaped estuary, they can be noticeably influenced by terrain uplift and estuarine convergence, resulting in a distinctive phenomenon characterized by a rapid rise in water level, commonly referred to as a tidal bore. Tidal bores can propagate at high velocities and are typically associated with substantial sediment transport, which can induce significant erosion and deposition on the riverbed within a short time. Concurrently, abrupt variations in riverbed topography can exert a pronounced influence on the propagation and evolution of tidal bores. Previous studies have predominantly focused on the propagation and evolution behaviors of tidal bores over gently flat topography, whereas investigations into their characteristics over abrupt topography remain limited. In this study, a high-resolution numerical simulation approach is employed to systematically investigate the propagation characteristics of tidal bores over abrupt topography. The effects of initial water depth, incoming tidal bore height, and variations in topography are examined in detail. Furthermore, theoretical approximate solutions for the tidal bore height and propagation speed over abrupt topography are derived based on the continuity and momentum equations of fluid dynamics. Results indicate that abrupt topography can significantly influence the tidal bore height, propagation speed, and bore front profile. Specifically, terrain uplift tends to progressively intensify the breaking strength of bore front, whereas terrain depression can reduce the breaking intensity and may even lead to a transition from a breaking tidal bore to an undular tidal bore. Validations further show that the theoretical approximate solutions for tidal bore height and propagation speed both demonstrate high accuracy and are suitable for corresponding engineering application and rapid assessment.