Bagworms are actually caterpillars from various moth species. They make a cocoon-like bag in which to live, while they hang on the branches of trees and shrubs to feed. Typical insecticides will have no effect when sprayed on the bag full of caterpillars. The bag structure itself will prevent any insecticide from entering, therefore rendering it harmless. Ideally, bagworm control should be done in the late fall or very early spring. At this time, the unhatched eggs will still be inside the bag and can be effectively coated. In this scenario, relatively harmless dish soap will work just as well as any chemically manufactured insecticide.
Add 2 tbsp. of dishwashing liquid to 1 gallon of water. Mix together thoroughly.
Pour the dishwashing solution into a garden sprayer. Close the cover and pump it up until there is good spraying pressure coming from the nozzle.
Find a good solid stick that is length appropriate. Make sure it has a pointy end to puncture the bagworm bags and it is long enough to reach them.
Puncture the side of the bagworm bag with the pointy end of the stick. Spray some dishwashing solution inside the bag, covering the inside as best as possible. When finished, move on to the next bag and repeat the process.