I doubt if you'll have enough heartwood left if you take all the sapwood off. I would remove the bark, then pick a side for the back (heart of the stave is off-centered, I would choose the thinnest ringed side for the back), flatten it down to the heartwood, then chase the first heartwood ring the full length of the stave. That's called decrowning. Here, part of the sapwood remains as the bow's back, but still you're following one continuous ring from end to end.
If still green, and with the bark removed, the sapwood will start checking fairly quickly. Keep things varnished up to prevent this when you're not working on your bow. And yes, the stave will dry with a coat of varnish/glue/wax/shellac or whatever else you choose to use.
You goal at this point should be, remove the bark, flatten the back and start roughing the bow out. Get the roughed out bow to where it's limbs are bending a little, coat the entire thing and lay it back for drying/seasoning.
Probably need to make a bending/working handle bow of some sort but first things first.....Art