Did it between P'Burg and I-90 in the opposite direction in 2011.
Heading in your direction, the first 10 miles or so of Rock Creek Road is paved. You will pass an outfitter called Trout Bum that has a coffee bar and snacks. It's the only place to get snacks until P'burg. (You will pass a couple of U.S.F.S. campgrounds that I believe have water.) Take a walk out onto the cable and plank bridge you will pass on your right. Then there is about 30 miles of dirt (IIRC) to the junction of MT 348 that takes you to P'burg. The road conditions car vary the father up you go due to the creek spilling its banks. I was riding 37c tires and did a bit of slipping and sliding in the dirt early on. Also, the U.S.F.S. puts down calcium chloride on part of the road to keep the dust down. This can create a slightly wet/muddy section. We stayed at Ekstrom Stage Station at the end of the day and had to wash off our bikes. There were also a few sections with rocks, but they weren't long. I have never toured on 28c tires so I don't want to discourage you, especially since it's a beautiful ride, but it might be tough going in spots.
Here are some photos I assembled for someone else who asked abut the road:https://www.flickr.com/photos/davez2007/sets/72157647572217733/
MT 348, which is paved, is going to involve a short but stiff in places climb to get over the ridge. Here is a route map with profile:http://ridewithgps.com/routes/7503410
You will know you are there by the sign naming the bridge in honor of a local resident who died in Iraq. It's not far after you pass a B&B.
The campground/motel in P'burg is nice. There is a spot by an equipment shed that offers shade and has Adirondack style chairs and Purple Martin houses attached to a fence. The grocery store is basically right across the street from the entrance, and you can walk into the center of town. Don't miss the old ice cream parlor in town. I was there again last year. Good milkshakes.
The first 10 or so miles on MT 1 out of P'burg (up to the junction with MT 38) is pretty easy but then things get steep for a while. The latter part of the climb is exposed. Riding towards P'burg we stopped to talk to a couple of people riding up in the intense, afternoon sun. They were pretty knackered. Once you get up to Georgetown Lake it's flat and then, shortly after you pass Silver Lake, all down hill to Anaconda. If you need water as you are descending there is a plumbed spring just off MT 1 right before the interpretive sign for an old gold strike. You will see a paved road that bears down hill on the right. The spring is a short distance down there. You can leave you bike at the sign and walk down it's that close.
How do you plan to get back from Anaconda?