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 autumn. 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 30cm of root ball for every 2.5cm of stem caliper. .Don’t be afraid of cutting a few roots when you transplant. Just try not to cut them any shorter than the above guidelines allow. Cutting the roots will actually help to reinvigorate the plant. It’s a process simply known as root pruning. When the roots are severed, the plant then develops lateral roots to make up for what is lost. These lateral roots are more fibrous in nature, and have more ability to pick up water and nutrients.
Some nurseries drive tractors over the plants in the field with a device that under cuts the roots of the plant just to force the plant to develop more fibrous roots. This make transplanting the plant the following year much more successful, and makes for a stronger and healthier plant.
The old timers root pruned by hand by forcing a spade in the ground around their plants. If you have a plant in your landscape that is doing poorly, a little root pruning while the plant is dormant could bring it around. It’s worth the effort.