I'm not a whole lot of help with bear hunting, but welcome to BGH!

Wherebouts are you referring to when you say southern NM? That's a whole lot of country, plenty of it with bear.

Either the Gila National Forest or the Lincoln National Forest...

Thanks

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.

Thank you all for your replies, I will consider them if I get to go bear hunting.