Every zombie Movie/TV Show, has different rules, but in the world of the TWD, that would be wrong.
Everyone has the virus in them already, but in small doses, so if you die of natural causes you still turn.
If you get bit though, the bite introduces a large dose of the virus which is strong enough to cause a true infection, illness, and death.
In the books they use zombie gunk (blood, muscle, organs, etc..) to "infect" the weapon, then use the weapons on enemies. By piercing the enemy with an infected weapon (arrow, knife, etc..) it still causes illness and death. Nothing to do with bones.
The show seems to work different though. There are several scenes where characters get the zombie blood all over their faces without turning.