Bagworms are a feeding caterpillar that pulls bits of leaf or other material around itself using silk to construct a protective "bag" (camoflauged cocoons up to three inches) which it carries around, like a hermit crab's shell. The caterpillar comes out partially to feed but retreats inside the bag most other times. Pupation takes place in the bag and eggs are laid and overwinter in the bag. During pupation the bag is permantly attached to a tree branch via a strong tether of silk.
Control of the bagworm depends on the season. If it is early summer they may be controlled with appropriate insecticides, best of all is Bt Bacillus thuringiensis} which only harms caterpillers . For any insecticide to work it must be applied during the active feeding phase in early summer ( June 15 to July 15).
Pupating worms and the resulting moths are not susceptible to insecticide.
At any time the bags may be hand picked and destroyed.
The problem with bagworms is that they defoliate woody ornamentals, especially evergreens and that their "bag" is unsightly. I prefer to hand pick the bags as even Bt causes problems. The more desireable caterpillers of butterflies are also killed by Bt. Integrated pest management always calls for mechanical removal when possible.