Two to three summers ago, I rode from Homer to Fairbanks, then Prudhoe Bay to near Kitwanga, BC, before the forest fire smoke made me abandon my trip. I would suggest you do the Homer or Seward to Fairbanks ride. Reasons are much more services available (though admittedly limited in places) than the "eastern" part of Alaska. Also, winds are from the ESE through much of that corridor. If you have not finished by the time you have to get back, you can hop on the train with an unboxed bike in many places along the Juneau/Fairbanks corridor. Finally, you end up (after a train ride) back in Anchorage which is usually the cheapest and most direct place to catch a plane back to the lower 48. Oh, and you don't have to stress about hitching a ride.
I left Homer around May 30th. If you are looking for snow capped mountains, I would suggest in mid-May or the very earliest you can get a shuttle to Homer/Seward as the snow melts fairly rapidly as the summer comes on. Plus the mosquitos are less vicious compared to July. Note that it will be cool and you will need to camp a few times.
Traffic totally fine except for the stretch between 10 mile stretch south of Gateway. It was busy with a full shoulder but damn it was LOUD, probably the loudest I have ever been in. Could not figure out why either because it is wide open terrain there and the traffic type was the same as elsewhere. Just a lot more cars. It was a bit annoying around Denali but overall totally fine. Oh, all the roads were paved except for a few sporadic bits of road construction.
You should note that AK is fairly expensive, especially for hotels. When in Anchorage, I considered a hotel but a Motel 6, where 1/3 of the building was inhabitable due to a fire, was charging $295 + tax per night. Most hotels were in the $350-$450 range. WarmShowers is definitely something to consider in Alaska if they are available.
I saw some bears alongside the road but never had an issue or in the campgrounds.
Tailwinds, John