  Recent experimental realizations of bilayer boron materials motivated us to
study the structure and properties of $\alpha$-sheet-based bilayer borophenes
with interlayer covalent bonds. As shown here, at least three stacking
variations are possible: AA, AB, and AB$'$. The on-top AA-stacking has been
obtained experimentally. The AB-stacking is the most stable among neutral
freestanding structures, whereas the AA and AB$'$ stacking sequences are very
close in energy, both for neutral and negatively charged cases. The studied
bilayer borophenes exhibit extraordinarily high electric conductivity with
values as high as ${\sim} 10^7\mathrm{~S}/\mathrm{m}$ for the experimentally
observed AA-stacking. The highly stable AB-stacking bilayer, reported here for
the first time, exhibits an anisotropic conductivity with an average value of
$6.0 \times 10^6~\mathrm{S/m}$.
