Established Tree: Apple Planting Bush: Blueberries Goal: not damage apple tree root system Question: How do I plant a blueberry bush under an apple tree without damaging the roots of the apple tree?
So, it sounds like you're attempting to set up a guild around a mature tree? When you're setting up a guild, you really have to think about how all of the plants will interact, and what role the plants will each play in the guild. Other than your fruit tree, the plants you choose should either repel pests, attract beneficial insects, suppress weeds that would compete with the tree, either in the way they grow or because you can cut them down as mulch, or help accumulate nutrients. Some plants will fill more than one of these functions.
If you think about the blueberry and how it will fit into one of those roles, you'll realize that it won't. The blueberry will be demanding, and it will need different nutrients than the apple, so it would be competing rather than contributing.
So that means you need to think of different plants to go in your guild. One option for a shrub would be a goumi berry. It will give you fruit (which is why you'd chosen the blueberry, I assume) and it is a nitrogen fixer, so it will fit in the accumulator role. It is also vigorous and can take the shade of the tree. As others have mentioned, you can't safely plant it under the tree, but you could plant it just outside of the drip line. That will be close enough for the apple to take advantage of the extra nitrogen and it will decrease the chance of harming your tree.
You can't - if you want to plant close to a tree, it has to be done when you first plant the tree, at the same time, in other words. You could plant near the apple tree, but not under the canopy.