  We report the first observation of a large spin lifetime anisotropy in
bilayer graphene (BLG) fully encapsulated between hexagonal boron nitride. We
characterize the out-of-plane ($\tau_\perp$) and in-plane ($\tau_\parallel$)
spin lifetimes by oblique Hanle spin precession. At 75~K and the charge
neutrality point (CNP) we observe a strong anisotropy of
$\tau_\perp/\tau_\parallel$ = 8 $\pm$ 2. This value is comparable to
graphene/TMD heterostructures, whereas our high quality BLG provides with
$\tau_\perp$ up to 9~ns, a more than two orders of magnitude larger spin
lifetime. The anisotropy decreases to 3.5 $\pm$ 1 at a carrier density of n =
$6\times 10^{11}~$cm$^{-2}$. Temperature dependent measurements show above 75~K
a decrease of $\tau_\perp/\tau_\parallel$ with increasing temperature, reaching
the isotropic case close to room temperature. We explain our findings with
electric field induced spin-valley coupling arising from the small intrinsic
spin orbit fields in BLG of 12~$\mu$eV at the CNP.
