A loop with some fun singletrack descents through the Alabama Hills. The whole area is quite sandy, which is why the climb heads up the paved Whitney Portal Road, which you could choose to shuttle. Alternatively, people with fatbikes may enjoy climbing up off the pavement.
But the loop described should be enjoyable by all sorts of mountain bikes, with some fast, fun singletrack, cool rocks, and some exciting technical bits.
Just under five miles out of Lone Pine on Whitney Portal Rd, and at 5200 feet of elevation, turn off to the right to find the Upper Alabama Hills Trail singletrack that heads up above the Alabama Hills. This climbs another 400 feet of elevation before beginning a descent into the hills.
Continue downhill as the trail turns into a 4WD road, and continue right (downhill) as two other roads join in from the left. Soon (0.3 miles) after the second of these comes in, a singletrack crosses the road. Turn right to stay on singletrack, but note that this part is fairly sandy. If you have skinny tires or hate sand, you can continue on the two track to a wide gravel road (Movie Flat Road), and turn right to bypass this singletrack.
Either way will take you out to Movie Flat Rd at the Mobius Arch Trailhead. Turn left on Movie Flat Road and ride down for about half a mile to where it turns 90° left and up a hill. Look for The Horse Trail off to the right. This will take you up and down along some fun singletrack (with a bit of pushing) before you come out onto a 4WD road at a pass. Head down the east side of this pass and ride through the gully back to Lone Pine.