I've not had much experience with the Gila. I know the Lincoln forest near Ruidoso/Cloudcroft has a healthy bear population, but again, I'm not really familiar with the area. The Ranger district or the area game warden could probably help you out.
If you're coming from El Paso, you may consider the San Mateo mountains, unit 17. They are only an hour or so north of Cruces. I've done a lot of deer hunting in there and I see bears about every trip. Best bet would be to get up high towards Springtime campground or the Apache Kid wilderness where the Ponderosa pines grow, get on a high spot and glass the openings and little meadows. Spot and stalk opportunities abound.
Not the biggest bears in the world, but fun regardless.
If you want to properly preserve velvet antlers, you will have to inject & brush them with formaldehyde or some of the new less toxic chemicals (4 in 1 solution works great as does Knobloch's antler in velvet tan) as its easier to use however, both will work.
First, using rubber gloves take a razor blade and make small incisions at the tips of all points about 1/8". Next hang the antlers upside down, allowing the blood to drain. Starting at the bases inject the solution into the...