Bagworms winter over as eggs in the bag of the female from the year before. So the first measure of control can come by handpicking all the bags from last year.

These eggs hatch mid to late May through the end of June. Individual larvae drop from the bag on a strand of silk and either swing onto a branch or sail in the wind to another tree.
Immediately upon landing they build a silk-lined bag, often decorating it with bits of foliage

Larvae remain in the bag feeding, with only the head and thoracic segment extending out.  As the larvae grows, the bag expands to accommodate it. Mid to late August, feeding will stop and in two to three weeks adults emerge. Females remain in the bag looking like a slug. Males become a winged moth flying to the females bag and mating. The males die, female lays up to 1,000 eggs in her bag then dies as well.

Control is most effective starting early in the season when they first hatch out. Remember, little bagworms begin in, near the center of the plant, so use a hard spray and get coverage to the inner most part of the plant.
The Absolute Best control for Bagworms is Natural Guard Spinosad, or Spinosad Soap. This is a natural product so is very safe for kids, pets and wildlife.

The next best product is also a natural product, NG Caterpillar Killer Spray with Bt. This is only effective on worms and caterpillars.
Always make two applications 10 to 14 days apart. Also, due to the silky webs holding the bag together, add Spreader Sticker to the mix to increase adhesion, penetration and residue length. Direct the spray from the tip of the plant to the inner most part of the plant.

When the bags are over an 1½ inch long, the above controls are less effective, at this point you need to use HY 38 Plus. Again add Spreader Sticker and make two applications 10 to 14 days apart.