This paper develops a conservation-consistent framework for warp-bubble spacetimes within classical General Relativity. Rather than assuming exotic propulsion mechanisms or reactionless motion, the analysis treats propulsion, stability, and feasibility as internal mathematical constraints imposed by covariant conservation, distributional geometry, and boundary dynamics.Warp bubbles are modeled as Omega-isolated regions bounded by timelike worldtubes and treated as distributional solutions of the Einstein equations with generalized junction conditions. A total stress tensor is defined that preserves exact covariant conservation, allowing a clean separation between geometric curvature requirements and the sectors responsible for supplying them.A central result is a control-volume momentum theorem showing that any acceleration of a warp bubble is possible only through explicit boundary momentum flux. Reactionless or self-accelerating solutions are excluded by construction. Thrust is reinterpreted as controlled momentum export across the bubble wall, independent of coordinate choice or gauge.For a broad class of conformal warp geometries, explicit Einstein-tensor expressions and null-energy-condition diagnostics are derived, yielding thin-wall scaling laws that convert qualitative exotic-matter discussions into quantitative inequality constraints. Feasibility is shown to be governed by three independent constraint families: quantum-inequality bounds acting only on the ordinary stress sector, curvature and tidal limits imposed by geometry and observer safety, and momentum-flux constraints that restrict admissible acceleration profiles.A coordinate-invariant spectral criterion is introduced to diagnose genuine isolation of the bubble interior and its stability under actuation, providing a falsifiable test for candidate metrics. The framework makes success and failure sharply decidable and treats warp bubbles as well-defined mathematical objects subject to explicit conservation laws rather than speculative assumptions.This work is intended as a foundational, conservation-first model for analyzing localized spacetime propulsion within General Relativity. Engineering realization and specific energy-source proposals are deliberately separated and treated as external to the geometric framework.https://doi.org/10.5281/zenodo.18014526