I have to agree with the previous posts that Slough Creek gets a lot of use - too much most of the time. It is a fairly easy place to catch fish, though not any easier or more difficult than other park streams with Yellowstone cutthroat in them. Any of the meadows, and even the river below the meadows, are good places to fish.
As for bears, you should take appropriate precautions anywhere in the park - i.e. make lots of noise, carry bear spray. You have better chances of being hit by lightning than a bear harming you. Hiking alone is not the best idea, not only because of the bears, though the Slough Creek meadow hikes are relatively easy and heavily travelled.
As for flies that will work in August - you'll catch fish with caddis or rubber leg attractors, like a Turck tarantula in smaller sizes (8-12). These cutthroats aren't difficult to catch despite some folks' magazine articles to the contrary.