I pick out out one with great horz. arched rings.
(...)
with about 8 to 10 rings per inch.
This is basically totally irrelevant in ipé. Ring orientation is of no importance since the wood is very uniform. Ring count also does not matter with this wood, since it is not ring porous, nor does the density or quality depend on the amount of rings per inch (as it does with for instance yew). You just need to pick a straight grained board without any knots. In that aspect, picking a board of ipé is much easier then picking a board of ash or oak. Ignore the RINGS in ipé, but pay attention to the GRAIN.
Ipé can be used unbacked, but it is not easy. With your board and experience, I would advice you to use a decent backing. White oak, hickory or bamboo will all work beautifully, but even ash or maple could be used. You just create a flat surface and glue on a lamination as a backing.
If the 2x2 is REALLY 2x2 and not 1½x1½, then you might be able to get even four slim bows out of it. Each will be slightly under 1" wide then, which is sufficient for 50# in the hands of an experienced bowyer. However, in your situation you might be better off cutting the board once through the center, so you'll get two boards of roughly 2x1. Plenty to a 100# bow. In practice, I would rip the board to 1¼" x 3/4" before backing.
