This route requires less bushwhaching than ascenting from the east slope, but is considerably steeper.
Timberline Pass from Ute Meadows
To reach the jumping off point for this route, you will want to start at the Upper Beaver Meadows TH. Follow signs for the Ute Trail. Hike the trail ~2.5 miles past well marked intersections keeping in mind that you are heading towards Timberline Pass. You will pass the Ute Meadow Llama campsite sign, anywhere past this point is fine to leave the trail
West slope up Beaver Mountain
From Ute Meadows, one must simply scramble up the side of the mountain, heading slightly NW to gain the ridge somewhere near the summit. The scramble is not exactly easy, the terrain consist mostly of small rocks, loose sand and gravel and downed trees. Depending on how much fun you want to have, you can either skirt the small rock outcroppings on the side of hill, or just climb right over them.
I would rate this as class 2+ just because you're not exactly in the realm of climbing, but it is steep frustrating bushwhacking. I have done this route twice and have never had a problem, but I advise you gain the ridge somewhere near the summit, not right at the base of the outcropping, lest you want to make it a whole lot harder.
Looking back down to Ute Trail
Good routefinding skills along with seasonal equiptment