I have not taken the traditional East face route to the summit but, from what I understand the difficulty level is similar. This route covers more mileage but may also be a better option during times of the year when snow and ice may require crampons and an axe. One also may need to improvise certain sections of this route as specific gullies I took are extremely difficult to describe. Nonetheless this is a fun, moderately strenuous day hike with about an hour of scrambling involved. On a clear day rewarding views of the Crazy, Gallatin, Madison, and Tobacco Root Mountain ranges can be seen from the summit.
From Bozeman, take Bridger Canyon Road North past the ski mountain and take a left on Forest Service Road 631. This road can be taken almost all the way to Ross Pass if you have a high clearance 4WD vehicle. From here take Ross Pass Trail for a little less than a mile to the ridge.
Follow the steep ridge up from the trail to where it becomes all rock. At this point it becomes scrambling with and slightly deviates to the west face where there are numerous small gullies with lots of loose talus. It's very difficult to describe my specific route from this point on, but it sort of zig-zags through these gullies gradually until you come back onto the main western ridge and can easily walk to the summit. I took my dog who struggled but made it. I would not however choose to bring him again on this route.
No specific climbing related gear is needed if you are experienced in moderate scrambling. Tennis shoes will suffice.