It seems somebody lost a fly on a tree limb as they floated down the river, and this bat flew by and attacked it and got stuck. Either that, or the bat caught their fly as they were fishing and wrapped it around the limb as he was fighting to get away. Either could happen, although the former possibility is a bit more likely.
Troutnut.com is a collection of pictures and information about fly fishing. Fly fishermen, fly tiers, and trout enthusiasts of all stripes can learn more about life beneath the surface of trout streams, as well as how to better imitate aquatic insects with artificial flies to catch trout. There are aquatic insect pictures, underwater pictures, landscape pictures, and a comprehensive reference to the common names of trout stream insects.