Singletrack in this area is hard to come by, but there are a lot of jeep roads that make good rides. The Dona Ana Mountains have a lot of roads that don't show up on the map provided by this website. Recently someone has also been blazing a bunch of new single track in the area shown on the map. I don't know if the BLM has approved the new singletrack, but I suspect not. I would prefer that trails be pre-approved, as Shane Cunico did, so that we don't piss off the BLM.
For another good ride, go north on I25 to the Radium Springs exit. Turn right, go about 100 yards, and park. There is a dirt road that continues on north, roughly paralleling I25. Follow the road until it crosses a cattle guard, probably about 1/4 mile. A dirt road turns off to the right and heads for the north end of the Dona Ana Mountains. There's a lot of good riding out there, tho I usually wait until right after a rain because some of it is pretty sandy. There are some indian petroglyphs in the area that make for a good diversion. Look for them in a deep arroyo beneath the power lines, and again near the base of the Dona Ana's. Someone has been trail blazing in this area also. I doubt that it's approved trail, so I don't recommend using the single track until someone has worked it out properly with the BLM.