Mulberry is good. My experience is with red mulberry. Makes a good flatbow. I have a very nice stave of red mulberry, and some unknown mulberry staves (white or red??), drying right now.
I like the sapwood off. Growth rings are usually so thick that following a ring is very easy..idiot proof really.
Treat like Osage, but design it about 15-20% wider.Osage flatbow dimensions are on my site, if you're looking for ideas (
http://analogperiphery.blogspot.com/2008/05/osage-flat-bow-dimensions.html) Take those measurements, but make it 1.75" or so at the flares and gradually taper from there.
I'm currently working on a post about drying wood. That should be in a few days. But for now, I'd seal the ends of the staves, store them indoors or in shelter with 50-60 average RH. In such conditions, wood dries at about 1" of thickness per year. Full sized staves take a few years.
You can work a stave down to a bow blank and clamp it to a 4X6. Let it dry that way and it should be ready in a few months (4-6). You can speed things up a little but if your do some floor tillering before clamping it to a 4X6..that should get you dried in about a month or two. Any faster and you'll have to use a hotbox of some sort…I'd don't care for those…to easy to bugger it up and overdry it.
Above all, though: seal those ends of the stave or roughed out bows. Whether the back is sapwood or heartwood, seal the backs if the bark comes off.