What is the difference . . .?

Question

What is the difference between a bush and a shrub? And at what point does a shrub become a hedge?

Answer 1

While technically a bush and a shrub describe the same type of plant, a bush is considered to be somewhat smaller than a shrub.

The point at which a shrub becomes a hedge is when the shrub is closely planted with others shrubs and pruned into a sort of wall or fence.  Typically of three or more feet high.  

But in a more slang way, the difference is where it grows:

It is a shrub if it grows in the garden and a bush if it grows on your body.  

^-^

Answer 2

With regard to your first question, there is no actual difference. Bush is the layman's term for shrub, which has a specific meaning in the botanical literature. Similarly, hedge is again a subjective layman's term for a row of shrubs growing together to form a wall/fence of sorts. At what point one calls a number of shrubs (or small trees) growing closely together a hedge will depend on the context.

Shrub: A woody plant of relatively low height, having several stems arising from the base and lacking a single trunk; a bush.

Hedge: A row of closely planted shrubs or low-growing trees forming a fence or boundary.

Source: Answers.com