1. I highly recommend Nancy Pallister's "Beyond Trails in the Wind River Mountains." Do get the accompanying CD which has far clearer maps and photos that you'll drool over. Be sure to read her introduction, study the descriptions of the routes and carefully assess your skills. Since you say you have no glacier travel experience, I'd avoid anything that goes over a glacier, especially solo (definitely not advised for glacier travel). The glaciers will be mostly bare ice and snowfields will be icy for part of the day when you plan to go.
2. There is often a snowstorm about Labor Day. After that the probability of thunderstorms is less but the probability of significant snow is greater. Of course last year it snowed a foot (per reports) in Titcomb Basin on Aug. 8 and Aug. 15, so going earlier is not a guarantee of no snow! Best to be prepared! The locals may tell you that after the Labor Day storm, you'll have several weeks of warm sunny days and clear COLD nights). Personally, I wouldn't count on it!
3. No bus into Pinedale. There basically isn't much public transit in Wyoming, a very sparsely populated state. The shuttle services on the west side of the Winds and to the Jackson or Rock Springs airports are provided by the Great Outdoor Shop in Pinedale. Not cheap, but excellent service. Their phone number is on their website.
4. Check the Bridger-Teton National Forest website. The rules are to hang or use a canister. Frankly, I used my Ursack because I can't throw (arthritis and lack of skill) and no way could I carry two canisters (one for me and one for my dog's food). I never saw any sign of a bear. Some grizzly have been sighted in the north end of the Green River Basin (north and east of Green River Lakes). A few places have problem black bears--Golden Lakes, Big Sandy Lake, Cirque of the Towers.
One thing you should know is that most of the lower and mid-level forest in the Winds is lodgepole pine, which has pretty well been killed off by the bark beetle epidemic. The result isn't pretty, but you get used to it. You thus may have problems finding a safe place to camp at lower elevations, and will probably have to camp in a meadow. Up in the high country, no problems with the trees, but there is a lot of area above timberline with no shelter except boulders, so you need a tent that will stand up to wind. Just yesterday Elkhart Park reported 45 mph. wind gusts. I'm sure they were a lot stronger higher up!
The Earthwalk Press maps are excellent for planning but lousy for details. I'd download and print out the appropriate USGS maps once you figure out your route.
I'd plan a couple of layover/contingency days into your itinerary in case of bad weather (you don't want to be crossing a 12,000 foot pass in a blizzard whiteout). It's also a good idea to have a bailout plan just in case.
One other thing--altitude. The Elkhart Park trailhead is 9300 feet and you'll be well above 10,000 feet the first night. Know the symptoms of Acute Mountain Sickness and descend immediately if they happen. Otherwise, you'll mostly find that you get really tired. Plan to take it easy the first few days.