= Solution
Let $a$ denote the bubble size, $U$ its speed, and $\operatorname{Re}=Ua/\nu\gg1$ the <Reynolds number>. Outside a thin <boundary layer>, inertia dominates and the flow is an <irrotational flow> with velocity scale $U$ and strain scale $U/a$. Its viscous dissipation has order
$$
\mathcal D_{\rm outer}
\sim \mu\left(\frac Ua\right)^2a^3
\sim\mu U^2a
$$
in three dimensions.
The boundary-layer thickness is
$$
\delta\sim\left(\frac{\nu a}{U}\right)^{1/2}
=a\operatorname{Re}^{-1/2}.
$$
For a clean bubble the <stress-free boundary condition> prescribes tangential stress rather than tangential velocity. The outer flow already has tangential strain of order $U/a$, so cancelling that stress requires a velocity correction of only
$$
\Delta u\sim\frac Ua\delta,
$$
not a correction of order $U$. Its gradient remains $O(U/a)$, and its boundary-layer dissipation is
$$
\mathcal D_{\rm layer}
\sim\mu\left(\frac Ua\right)^2a^2\delta
\sim\mathcal D_{\rm outer}\frac\delta a,
$$
which is asymptotically smaller.
In steady translation, the drag power $DU$ balances viscous dissipation. The leading estimate therefore follows from the known outer flow alone:
$$
\boxed{D\sim\frac{\mathcal D_{\rm outer}}U\sim\mu Ua}
$$
in three dimensions. This is the <dissipation estimate for high-Reynolds-number bubble drag>.
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