  In gapped bilayer graphene, similarly to conventional semiconductors, Coulomb
impurities (such as nitrogen donors) may determine the activation energy of its
conductivity and provide low temperature hopping conductivity. However, in
spite of the importance of Coulomb impurities, nothing is known about their
electron binding energy $E_b$ in the presence of gates. To close this gap, we
study numerically the electron binding energy $E_b$ of a singly charged donor
in BN-enveloped bilayer graphene with the top and bottom gates at distance $d$
and gate-tunable gap $2\Delta$. We show that for $10 < d < 200$ nm and $1 <
\Delta < 100$ meV the ratio $E_b/\Delta$ changes from 0.4 to 1.5. The ratio
$E_b/\Delta$ stays close to unity because of the dominating role of the bilayer
polarization screening which reduces the Coulomb potential well depth to values
$\sim \Delta$. Still the ratio $E_b/\Delta$ somewhat decreases with growing
$\Delta$, faster at small $\Delta$ and slower at large $\Delta$. On the other
hand, $E_b/\Delta$ weakly grows with $d$, again faster at small $\Delta$ and
slower at large $\Delta$. We also studied the effect of trigonal warping and
found only a small reduction of $E_b/\Delta$.
