$bto stau^+tau^-$ measurements are highly motivated for addressing lepton-flavor-universality (LFU)-violating puzzles such as $R_{K^{(ast)}}$ anomalies. The anomalies of $R_{D^{(*)}}$ and $R_{J/psi}$ further strengthen their necessity and importance, given that the LFU-violating hints from both involve the third-generation leptons directly. $Z$ factories at the future $e^-e^+$ colliders stand at a great position to conduct such measurements because of their relatively high production rates and reconstruction efficiencies for $B$ mesons at the $Z$ pole. To fully explore this potential, we pursue a dedicated sensitivity study in four $bto stau^+tau^-$ benchmark channels, namely $B^0to K^{ast 0} tau^+ tau^-$, $B_stophi tau^+ tau^-$, $B^+ to K^+ tau^+ tau^- $ and $B_s to tau^+ tau^-$, at the future $Z$ factories. We develop a fully tracker-based scheme for reconstructing the signal $B$ mesons and introduce a semi-quantitative method for estimating their major backgrounds. The simulations indicate that branching ratios of the first three channels can be measured with a precision $sim mathcal O(10^{-7} - 10^{-6})$ and that of $B_s to tau^+ tau^-$ with a precision $sim mathcal O(10^{-5})$ at Tera-$Z$. The impacts of luminosity and tracker resolution on the expected sensitivities are explored. The interpretations of these results in effective field theory are also presented.
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