You did good by allowing your wood to dry. Though I would have at least split them in half so they would lose excess moisture. Green wood can be easier to work with hand tools, but power tools do better with dry wood and good bows are made with wood brought down to 7-10% moisture content. If wood that is wet or 'green' is bent, it tends to stay bent rather than spring back the way a bow needs to do. So you did good there by waiting. If they sat with the bark on though, in log form, they still may not be dry enough to begin bending.
That said, you can quickly bring a green stave to oversized bow dimensions so that it sheds moisture faster, allowing you to finish out the bow sooner than if it was say, just split in half. The vine maple I've used I split and dried first.
By concave side, if you mean you dried the wood in the form of a little log, and as it dried it bowed so that both ends are pointing toward the same side, and you're calling that the concave side??? Then yes, that is usually the tension side of the tree and will make better bows.