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.
One for the Young at Heart in trying.
Whitetail hunting can be fun when you and a hunting partner want to make for some fast action during mid day hunts after morning stand hunting is over and waiting for your evening hunt. Few years back I wanted to demonstrate one of my methods to my son how two guys can make for some fast action during mid day hunting. The set up is for two people when the crops are usually off and the only cover left is...