Is the wood dry at this point? Growth ring orientation like that (lopsided) can seriously warp staves. Those rings are not 'bad' per se, but it makes for more difficult bowyery. Normally, the rings 'feather out' on the belly of a bow, but those will not happen in this case. Furthermore, one side of the limb may be denser wood (=smaller rings) than the other side. That might mean the limb twists easily. You could very well end up with on side of the limbs thicker than the other wide, but that will become clear during tillering.
It's a nice stave with potential. With a growth ring orientation like that, you just need to be carefull because the wood is not uniform in the stave. With a branch (any wood), you should ideally take either the top quarter, pointing towards the sky, or the bottom quater, pointing towards the earth. The "left" and "right" quarters/sides should be tossed away.