From the trailhead, it makes the best sense to just walk along the Mosquito Pass road or follow nearby for most of the distance to the pass. Lower down, you could work off road but will have to contend with willows. Higher up, after the road passes the west ridge of London Mtn., you might as well stick with the road. Doing so will likely mean you'll have to deal with multiple vehicles passing by churning up dust and making noise, and you have to walk through all the loose rubble on the road.
From the summit of Mosquito Pass, Mount Evans B is a simple stroll along the ridge to the south for about 1.8 miles. You will pass some radio, broadcast facilities along the way. Most of the terrain will be tundra with embedded rocks and some scree and chiprock. Enjoy the expansive views both east and west. Overall, if you're going to use the Mosquito Pass road on either side to access Mt. Evans B, we consider the east side approach to be the least desirable. See the next paragraph for two other hiking suggestions.
A. Take the same driving approach for the east side of Mosquito Pass as described in the trailhead, but instead of driving the last couple miles, turn off to the west on CR 696 that goes SW up South Mosquito Creek to a mining operation. Before the mine, 696 veers off to the right, climbs a short switchback and then heads into "American Flats." Park where you will, beyond any private property, perhaps near a small pond at 12,140 ft. Identify the summit of Mt. Evans B and make a beeline for the summit SW across the mostly tundra terrain. You'll likely end up on a broad NE ridge of Mt. Evans that will bring you out north of the summit for the finale. One-way mileage would be reduced to about 1.75 with no more than 1,400 vertical gain. This route has not been field tested. There may be private property concerns.
B. The other suggestions combines Pennsylvania Mountain with Mt. Evans B by a ridge that connects those two summits. Follow driving directions for Pennsylvania. From the summit of that mountain, walk generally west along the ridge to a saddle between it and Evans B. The drop to the saddle will harbor the only rocky section to deal with. Then follow the east facing slope up to Evans B. You can make most of the ascent on basically tundra terrain.