I agree with Pat. I sinew back a bow when it is part of my initial plan for the bow. I won't waste valuable, especially time consuming sinew attempting to fix a bow that didn't turn out well. Study what went wrong, take the lessons learned, then build a better bow the next time.
On moisture content, I'm not a technical kind of bow maker. I don't spend a lot of time on forced draw curves, grain weights of arrows and moisture meters. I've built a bunch of osage bows. If you're starting from a quarter split stave, you should wait at least a year before making a bow, start to finish. Period.
However, You can reduce the seasoning period significantly through methodical reductions of the wood from the original quarter split. When you're removing any wood, you're also removing moisture content, right? Less wood, less moisture to deal with. But you shouldn't rush this either. First, peal the bark, sapwood and establish a growth ring. Apply glue or cheap sealer to the established growth ring (back of the bow). Wait a couple two or three weeks. Then I'll draw out a bow on the back. I'll cut out the bow leaving a 1/4-inch outside of the lines that I drew. Then I glue/seal the sides and wait another couple two or three weeks. Then I'll cut closer to my lines and also cut the belly shape so that I am prepared for floor tillering. Wait again, 2-3 weeks. At this phase, if you steam the bow and clamp it to a form, you can take out undesirable kinks, propeller twists, etc. The added benefit though is that steaming seasons the bow further, driving moisture out of the wood. There are physics involved in why this happens which I do understand technically, but this is a primitive website and most times the technical hubbub bores me.
That being said, remember that it doesn't matter to the wood how long it takes to become a bow. Our best bows are those we spent the most time on.