Early spring is a great time for transplanting trees and shrubs, but you must do so before they wake up. Transplanting a plant is a very traumatic experience for the plant if it is awake. Its like doing surgery on a person while they are awake. Dormancy starts in the fall as soon as you experience a good hard freeze, and the plants remain dormant until the weather warms up in the spring. This is when you should transplant, while the plants are dormant.
You can transplant in the spring up until the plants leaf out. When the buds are green and swollen you are usually safe to still transplant, but once the leaf develops, you should wait until fall. When transplanting you can dig the shrubs out bare root, just make sure they are out of the ground for as short a time as possible, and keep the roots damp while out of the ground.
Make sure there are no air pockets around the roots when you replant them. When possible, it is always better to dig a ball of earth with the plants when you transplant them. The rule of thumb is 12 of root ball for every 1 of stem caliper. If the diameter of the stem of a tree is 2, then you should dig a root ball 24 in diameter.