  We report the magnetic structure and electronic properties of the honeycomb
antiferromagnet $\rm NaNi_2BiO_{5.66}$. We find magnetic order with moments
along the $c$ axis for temperatures below $T_{c1}=6.3(1)\>{\rm K}$ and then in
the honeycomb plane for $T < T_{c2}=4.8(1)\>{\rm K}$ with a counterrotating
pattern and an ordering wave vector ${\bf q}=(\frac{1}{3},\> \frac{1}{3},\>
0.15(1))$. Density functional theory and electron spin resonance indicate this
is high-spin Ni$^{3+}$ magnetism near a high to low spin transition. The
ordering wave vector, in-plane magnetic correlations, missing entropy, spin
state, and superexchange pathways are all consistent with bond-dependent
Kitaev-$\Gamma$-Heisenberg exchange interactions in $\rm NaNi_2BiO_{6-\delta}$.
