Accretion onto central massive black holes in galaxies is often modelled with the Bondi solution. In this paper we study a generalization of the classical Bondi accretion theory, considering the additional effects of the gravitational potential of the host galaxy, and of electron scattering in the optically thin limit. We provide a general analysis of the bias in the estimates of the Bondi radius and mass accretion rate, when adopting as fiducial values for the density and temperature at infinity the values of these quantities measured at finite distance from the central black hole. We also give general formulae to compute the correction terms of the critical accretion parameter in relevant asymptotic regimes. A full analytical discussion is presented in the case of an Hernquist galaxy, when the problem reduces to the discussion of a cubic equation, therefore allowing for more than one critical point in the accretion structure. The results are useful for observational works (especially in the case of low-luminosity systems), as well as for numerical simulations, where accretion rates are usually defined in terms of the gas properties near the
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