I agree with blackhawk here. At 1/8" at the tips, it is simply too thin to make a good belly. At 3/8" at the center, it is simply too thick to work as a core. You should have worked out your dimensions better. You could, however, use one barrel tapered and one uniform 1/4" walnut lam to glue up a maple/walnut/walnut bow. I would recommend you to use maple as a backing, or even ash. Walnut is just not strong enough for a bamboo or hickory backing.
By the way, I disagree with squirrelslinger that walnut is a whitewood. It is not, in my opinion. Although the definition of 'whitewood' is very vague, I personally believe it is always a non-heartwood forming tree.