  We investigate the superconductivity (SC) driven by correlation effects in
electron-doped bilayer BiH near a type-II van Hove singularity (vHS). By
functional renormalization group, we find triplet $p$-wave pairing prevails in
the interaction parameter space, except for spin density wave (SDW) closer to
the vHS or when the interaction is too strong. Because of the large atomic
spin-orbital coupling (SOC), the $p$-wave pairing occurs between equal-spin
electrons, and is chiral and two-fold degenerate. The chiral state supports
in-gap edge states, even though the low energy bands in the SC state are
topologically trivial. The absence of mirror symmetry allows Rashba SOC that
couples unequal spins, but we find its effect is of very high order, and can
only drive the chiral $p$-wave into helical $p$-wave deep in the SC state.
Interestingly, there is a six-fold degeneracy in the helical states, reflected
by the relative phase angle $\theta=n\pi/3$ (for integer $n$) between the spin
components of the helical pairing function. The phase angle is shown to be
stable in the vortex state.
