Stress Encourages Pest Problems
It is generally true that when bagworms attack a tree in sufficient numbers for you to begin to see damage and defoliation, then it is very likely that the tree was under some stress BEFORE the bagworms appeared. Pest insects prefer to go after weakened trees, ones that are struggling and lack vigor for some reason.

So after you deal with the bagworm problem, try to figure out what might be the causing the affected plant to be vulnerable to pest attack. It may be that it is not getting enough sun. The soil it is growing in might be terribly compacted, all the air having been compressed from it over the years by foot and mower traffic or the weight of nearby parked cars. The soil may be too soggy and never completely dries out. Spreading some organic material over the soil and core aerating the soil on your property adds air to it and helps it drain better to benefit all of your plants.

Other Conditions That Foster Bagworms
Bagworm populations are normally controlled by various birds and by a number of beneficial insects found in healthy home landscapes that host a diversity of plants and wildlife. Where there has been frequent use of broad spectrum insecticides which kill insects indiscriminately, nature’s first line of defense, the beneficial insects, is eradicated along with the pest insects. Since pest populations rebound faster than their beneficial predators, the bagworms are able to establish themselves without fear of attack. In yards where there are few resident or visiting predator songbirds bagworms multiply rapidly.