OverviewBourgeau Right is a classic climb accessed from the popular Sunshine ski hill parking lot. The route is subject to high avalanche risk so be sure to check the snow conditions. That said, it is a beautiful long climb with an alpine feel to it, and highly recommended. It presents two steep pitches, followed by steps of easier ice and snow climbing that gets you up high.
Getting ThereFrom Banff, follow the Trans-Canada highway west, until the turnoff for "Sunshine", a big ski resort. Go to the regular ski parking lot, and the route will be visible on the right as you drive in. Try to find a trail up through the trees and basically aim straight up for the route. This often involves post-holing and in such conditions it can easily take 2 hours to slog up there. Be careful to bypass some cliffbands and/or scramble up rock to the base of the first pitch. Allow ample time to figure this out by starting early.
Some of the snow slopes between the pitches are steep and suspect, so be sure the conditions are good, and remember the route is threatened by a huge snow bowl from above as well. The route can be thin in places warranting the "R" rating specifically on the first two pitches. Ice anchors can't always be built, and there are some fixed pitons on route, but test them carefully before you trust them. The slings on them can also be ancient, so bring a lot of cord to build abalakovs and replace rotten old webbing when rappelling.
Rappelling is probably the best way to descend, but if there are many parties below you and you decide to, there is a walk-off described in the guidebook, which is subject to additional avalanche risk.