Both times it took me about 7.25 hrs. from Colonial Creek Washington Pass including rest breaks.
There is a U.S.F.S. campground relatively early on during the descent. In the Mazama area, a couple recently opened a cyclist-only campground on their property. It's on SR 20, so it might be off route as I think the official route uses a smaller road on the other side of the river for a while.
IIRC, the first 16 miles are pretty much screaming. Once you get to Mazama, it cools out to Winthrop, where there is a nice KOA along the river. When I was there, the owners were really nice. They gave me a "cyclist discount" and even offered to let me sleep in one of their Kabins for the same price. Winthrop is a good place to take a rest day after the climb.
OP: Something I forgot to mention. If you start somewhere like Shelby you are going to hit Going to the Sun pretty early. Probably about the third day unless you take the route proper and go into Canada, which is not easy. The ride from Cut Bank, MT, just west of Shelby, to McGrath, A.B., is a lonely one. IIRC, it's about 70 miles. The only thing in between was a small store in Del Bonito. Getting back into the U.S. via Chief Mountain is no piece of cake. Rode that direction in '09 as part of a loop from Whitefish . There is a very stiff climb of about 6 miles that starts not far from the road that takes you into Waterton Village. Then there is another climb up to the border crossing. When you finally make it to U.S. 89, you will likely have a major headwind to St. Mary.
If you skip Canada, ride from Cut Bank to East Glacier and take MT 49 and U.S. 89 to St. Mary, you will also have some climbing. MT 49 offers some gorgeous views:
http://www.flickr.com/photos/davez2007/3676639154/in/set-72157620763740044But there is a stiff climb up to the top, which is known as Looking Glass Hill. Fortunately, it's not super long. Taking U.S. 89 and possibly Starr School Rd. from Browning may be a flatter option. Never done it, so I don't know. Either way, there will be some ups and downs on U.S. 89 between the junction with MT 49 and St. Mary, but you finish a screaming descent of maybe 5-6 miles into town. After climbing it I took this shot looking back down towards St. Mary:
http://www.flickr.com/photos/davez2007/3676637404/in/set-72157620763740044The point of all this being that regardless of which direction you opt for, you are going to do some climbing relatively early on. In the end, it's a beautiful route no matter which way you ride it.