The west face of the northern-most buttress (Buttress #1) on Tremont Mountain is a fun and quick climb that can be ascended via many routes from class 4 to 5.hard, depending on how you want to go. The route described here is one I did, and I felt the climbing was low 5th class.
The route ascends weaknesses (cracks) and sloping ledges above great exposure. I soloed the route w/o rope so I cannot comment on how the route would accept pro, but it looked like there are many places to place gear (cams/nuts etc.). Most of the face goes at 4th class and above. The rock is very solid granite.
Tremont mountain is only at an elevation of 10,000' or so, but the route faces west providing spectacular views of the continental divide, the Indian Peaks wilderness, Mt. Evans, Mt. Bierstadt, Gray's & Torrey's and even Long's Peak from the top. Fortunately from these peaks, it is easy to spot incoming weather from the west.
I have named the prominent buttresses along the ridge top trending south from the true summit of Tremont mountain as #'s 1 - 3. This being said, "The Bear" would be buttress #2. I do not know whether or not these buttresses have proper names or not...I don't think so.
1: At the base of the west face on butt #1, choose your line to gain the lower ledges behind the large pine tree near center of photo. This is best done from the north (your left). Once on the ledges, traverse south (right) 'til the ledges disappear and look for weaknesses in the up direction.
2: Keep traversing south and up towards a lone pine on steep slabs. Once near this tree, find the crack system and climb it. This crack isn't too hard (5.2), but a fall here will drop you 50+ feet onto boulders. Ascend the crack for 15' and move to the right at the top.
3: Next, aim for a dead tree (if it's still there) first moving behind a large flake-like boulder. Find cracks/weaknesses to move up and around this tree, still bearing south and up, to gain another ledge system.
4: From here, the easiest way is still to the south and up by following broken rock/ledges and more cracks towards a pillar.
5: Follow broken talus to the summit.
The easiest descent option would be off the back. The east faces of all the buttresses on this ridge are very slabby and go at 3rd & 4th class.
1: Walk east and then north descending into a few lone pines. Turn left (north) and walk along exposed ledges.
2: Where this ledge dead-ends into a wall, turn right and descend steep slabs.
This route lies wholly within Golden Gate Canyon State Park. A daily use fee of $5 U.S. is required and available at several self service kiosks within the park system.
The easiest and most direct approach is to enter the park from CO-119 ~6 miles north of Blackhawk on Gap Rd. Follow signs to the park entrance and the self-serve kiosk there. Turn right on Mountain Base Road and proceed ~1/2 mile to the first parking area you come to ( before the Bootleg Bottom Picnic Area!).
From your vehicle, head due west into the woods and straight up the hill. There is a lower elevation ridge (Promontory Ridge) that you will peak out on before getting to the top of Tremont. From here you can survey your surroundings and choose your line of ascent to the ridge proper.
Cams and nuts...standard rack if you're going to do it roped.
BETA PHOTO: Look back from above 1st ledges.
BETA PHOTO: Overview of 1st half of route.
BETA PHOTO: Middle of route. Aim for dead tree, if it's still...
BETA PHOTO: Descent route.
BETA PHOTO: Crux crack of climb near middle of route.
BETA PHOTO: More of the route from above.
BETA PHOTO: Looking back from above second set of ledges.
BETA PHOTO: Looking back from near the top of the route.
BETA PHOTO: Second half of route showing dead tree.
BETA PHOTO: Descent route from below.