  The choice of gauge in numerical relativity is crucial in avoiding coordinate
and curvature singularities. In addition, the gauge can affect the
well-posedness of the system. In this work, we consider the mean gauges,
established with respect to the geometric mean metric $h = g \,
(g^{-1}f)^{1/2}$ in bimetric relativity. We consider three gauge conditions
widely used in numerical relativity and compute them with respect to the
geometric mean: The 1+log gauge condition and the maximal slicing for the lapse
function of $h$, and the $\Gamma$-driver gauge condition for the shift vector
of $h$. In addition, in the bimetric covariant BSSN formalism, there are other
arbitrary choices to be made before evolving the system. We show that it is
possible to make them by using the geometric mean metric, which is determined
dynamically by the system, rather than using an arbitrary external metric, as
in general relativity. These choices represent opportunities to recast the
system in a well-posed form.
