There is no single universal "best" pest control solution for shrubs or any other plants. Differences in plant varieties and their requirements--as well as in locations and environmental conditions--make every situation unique. There are readily available toxic materials that are effective for killing insects no matter what the variables may be, but you might object to their effects upon your family and our environment. Many safe, simple household products have insecticidal properties, and can work as effectively for pest control as dangerous toxins do. The bottom line is that the best home remedy for shrub pest control is what works best for you.
Combine 1 1/2 cups of vegetable or mineral oil with 1 cup of warm water in a hand sprayer. Shake to mix well.
Add 1 tsp. of liquid dish soap. Stir slowly to blend, but do not create excessive suds.
Apply the insecticide to shrubs early in the morning to give it all day to work. This allows you to kill as many insects as possible during the hours that they're the most active. Oil insecticides work by coating the bodies of insects such as aphids, thrips, mealybugs, mites and scales. The preparations essentially asphyxiate the pests, killing quickly and effectively. But keep in mind oil insecticides don't discriminate, and destroy beneficial insect predators as well as the pests.
Coat all stem, leaf and bloom surfaces thoroughly, paying particular attention to the undersides where insects may be hidden from your view. Since this solution contains no harmful chemicals, it's safe to use on fruits meant for human consumption. So spray them for bug protection, too.
Repeat once each week for as long as you see pests on your shrubs. Reapply the insecticide immediately following rainfall during this time. Stop treating when you don't see bugs anymore. Resume spraying weekly if they come back.
Label and store the insecticide in a cool, dark spot.