We study the spin injection efficiency into single and bilayer graphene on the ferrimagnetic insulator Yttrium-Iron-Garnet (YIG) through an exfoliated tunnel barrier of bilayer hexagonal boron nitride (hBN). The contacts of two samples yield a resistance-area product between 5 and 30 k$\Omega\mu$m$^2$. Depending on an applied DC bias current, the magnitude of the non-local spin signal can be increased or suppressed below the noise level. The spin injection efficiency reaches values from -60% to +25%. The results are confirmed with both spin valve and spin precession measurements. The proximity induced exchange field is found in sample A to be (85 $\pm$ 30) mT and in sample B close to the detection limit. Our results show that the exceptiona...