Alright, may be a bit gruesome.
To get bones you will either have to kill an animal or anything that contains bones.
Animals will have a 99% chance of dropping bones when they die. But you would only get between 2-6 between kill.
When Eating meats such as dodo meat, and fish meat you will be subject to a 89% chance of getting a bone.
To make use of bones you will need to go to the press and press the bones down to bonemeal (Requires 10 bones to get 1 bonemeal)
From there you will need 10 bonemeal and a compost block to make an upgraded version of compost which makes plants and trees grow 6x faster then normal, and produce 10x more fruits.
In expert mode you will need 5x more bones except for compost.