Firstly, those are not bagworms... Bagworms attack evergreen shrubs mainly and build a sort of 'bag' around themselves as they are feeding. as the worm grows so does the bag.
I'm not a expert, but I think the pic is of webworm, usually called 'fall webworm' since it's active in the fall... The other worm that makes nests like that is the tent catipilar but they are usually seen earlier in the year and are dark in color. Both attack trees, but only certian species are singled out. Usually ash, walnut, mulberry, sweetgum, and crabs.
Tent catipilars and webworms are more ugly than anything. Come next spring the limb they were on usually leafs out again. They can be killed, easiest way is to just cut and remove them. Insecticides used need to penetrate the web via high pressure spray or by using something to tear it open prior to spraying.
An application of Bti (Bacillus thuringensis isrealensis) is exceptionally effective. It's not harmful to humans, pets, livestock, or beneficials. The brand I use is called Gnatrol and it has kept the webworms and caterpillars off my Passiflora quadrangularis for months. By the way, Arizweedhead, how the weather in Sedona right now? The little lady and myself are coming out to a b&b next weekend.