I have several of these trees on my property, and many grow in the area. I haven't made of bow from C Tallow wood. I have used the wood to make some small bowls. It works easily. Its a whitewood so it stains grey when not dried appropriately, and rots quickly too.
I wouldn't have thought it to be a good candidate for bows, it never grows really large, or has long trunks, before the canopy grows. Branches seem very brittle.
If you get a suitable stave out of what you have available, then I would go for a classic whitewood design to maximise your chance of success ie 2" wide limbs, flatbow