Short Answer
Dogs bury bones to preserve and protect them from other animals. They got this behavior from their wild ancestors who used to hide food by burying them into the ground because at that time it was challenging for them to find and store food.

Dogs have been at people’s side for longer than any other animal. But a lot of their actions can only be explained by their past before they were tamed by humans. For example, you may have noticed that a dog turns around three times on the spot before settling down to sleep this may be because its ancestors had to flatten down a nest in the leaves of the forests or jungles where they lived before they could sleep. And when a dog stands and bays, it may be doing what its ancestors did when they roamed in packs and had to keep in touch with one another. The same may be true of the bone burying routine.
For Dog’s wild ancestors, finding food was often a difficult task because it requires a lot of energy and time to catch their prey. After having food also, there was one big challenge that is other animals would be after the food. Therefore in order to keep others away from food, dogs used to hide their food such as bone by burying them into the ground. Burying food helped dogs in the protection and preservation of the food.
Before people fed dogs regularly, they had to hunt for food themselves, and burying it was the best way of keeping what they found, where their sense of smell could easily find it again.
Nowadays we know that dogs don’t have to bury bones or other food items because their human friend is also there to feed them.