Alaska's a big place, with different weather patterns in different zones. I've been a couple of times and seen snow in August on the North Slope (not much, but enough to cramp your style on a bike) and 90+ (F)/35+ (C) temps in Fairbanks shortly thereafter. The end of August is getting into autumn in the north and the bigger mountains.....and autumn is brief, just a week or two. Mid-september is getting pretty late for someone who doesn't like cold weather or camping in the rain.

On the plus side of the ledger, places that were crowded and roads that were packed with RV's just a few weeks earlier are relaxed and relatively empty. Bugs are not much of a problem that time of year until you get way south. It's a very pretty time of year, with colors changing rapidly on the tundra and wherever there are deciduous trees. There's still lots of light, but it also gets dark at night, so there's a good chance you'll see the aurora if you look for it. When it's not raining, that is.

The road back to the lower 48 passes through various ranges, and these, too, can be problematic in September and later. I've usually tried to stop in the Canadian Rockies on my return, and I've always hit at least some snow there.

IMHO, quality riding gear will be essential, since you'll likely be out in rain and cold. You need something that will keep you dry and warm all day; remember that in some areas there won't be a lot of places to pull over for a quick cup of coffee or to dry out. I'd budget for some motels from time to time, and remember that these can be expensive in some areas. There are also hostels in Alaska (a few) and Canada (relatively more).

I try to time my Alaska trips to arrive in early August and leave in the beginning of September, more or less, for all the positive and negative reasons above.

Hope that helps.

Mark