This out and back hike up Bear Mountain is the ultimate Sedona geology lesson. From the trailhead it appears you will be walking across a boring flat plain to get over to the mountain. In reality it's a roller coaster through deep-ditch-erosion. On the return trip, you get a beautiful view of these ditches as they spider across the desert floor.
In a little over a quarter mile you're at the base of Bear Mountain. The fun begins. You are starting in the lower section of Schnebly Hill Sandstone. It's a huffer 350 ft ascent to a deck etched out by Apache Limestone. As you're wheezing for air keep in mind you haven't even cleared a quarter of the climb yet!
You will notice the Schenbly Hill Sandstone is a tad lighter above the limestone. A good trail continues around the west end along this deck. In less than a quarter mile you come to a break in the wall. It's a short haul up a steep ravine. Edging out you may need to use some upper body for the final few yards.
Next you move across a more defined and distant deck covered with lots of manzanita. This deck is the split of Schnebly Hill Sandstone followed by Coconino Sandstone. When the incline picks up again in a half mile you'll notice the distinct difference. The Coconino is orange instead of red.
Continue to work up through approximately 500 ft of Coconino. Cairns become more plentiful. The first pine encountered is all by itself. This bad boy doesn't look old. Another look at all the pinecones strewn about makes you wonder. Further on is a real treat. It's a multi-directional etched-section-swirl of sandstone. This is unlike any other area around Sedona I've seen. It's more reminiscent of northwestern Arizona or Utah. Just fascinating.
At first it appears you'll get to go straight up through the heart of swirls. However, the cairns detour you right. Further up is yet another deck of sorts. I don't recommend exploring this deck, stick to the cairns. It's a maze of manzanita-lined-ravines of plate-rock. I might add, a topographical map would be wise for this hike. Continue up the last section. The footing becomes a bit more technical.
Once atop Bear Mtn you're on your own. It's a scraggly forest with thick bush and such. A trail does sort of skirt the outer edge. Work your way around. The views are breath taking every few steps. In sections, pitted Kaibab Limestone is cool as it lips the edge. Be careful, those aren't diving boards.
The top I describe is a tiny elevated island. You'll notice the bulk of Bear Mountain is further north past a saddle (which BTW is the break above the boxed-in-canyon-end of the Boynton Canyon Trail) It may be possible to work through the shrubs to either of those destinations. However, I think it'd be too painful. Instead you might try working around east at a lower elevation. I'll close with saying this isn't one of the tiny tourist attractions. It definitely qualifies as a must-do for the area.