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In this article, we present a generalized robust stability analysis for distributed bearing‐based formation control and network localization systems in a global reference frame. Different from many existing studies under ideal circumstances, we analyze stability of bearing‐based systems with general time‐varying exogenous disturbances. In addition to analyzing stability, explicit upper‐boundary sets of bearing formation control and network localization errors are derived via Lyapunov stability analysis. By computing the upper‐boundary sets of errors, we could obtain beneficial information for reducing and estimating the bounded errors. Since various sources of disturbances exist in reality, the research on robustness issues in this direction has potential benefits for practical applications to deal with system errors.