A bush is a little plant with many branches.
Ex: Fiona decided to plant a bush in front of her living room window instead of a tree so that the view from the inside wouldn't be obstructed.
Ex: As the children were playing hide and seek, one of the boys hid in a rose bush. He soon realised it wasn't a very good idea; he shrieked as the thorns pricked him, giving away his hiding spot.
In Australia and Africa, bush is used to refer to wild, untamed country or areas that have not been cultivated. The expression beat around the bush means to talk about something without mentioning directly.
Ex: When Victoria was growing up in Australia, she and her family lived in a remote house far out in the bush.
Ex: Some people might think that Amelia is a bit rude. The thing is, she doesn't beat around the bush; she always tells you exactly what's on her mind.
A hedge is a row of plants placed in very dense way. Ex: Olga lived in a planned community with very strict rules about landscaping. Every house had to have a neatly trimmed hedge along the front sidewalk and at least one tree in the front yard.
Ex: Fabio didn't want to put in a fence in his backyard, so instead he put in a hedge. That way, his dogs couldn't easily run away.
Hedge can also mean to protect one's self against a financial loss. A common expression with this verb is to hedge one's bets, which means that someone avoids committing to a side when faced with a difficult choice.
Ex: Oscar is hedging his investment by buying stock in two competing companies. That way, even if one stock declines in value, he'll earn money on the other.
Ex: Some businessmen hedge their bets during important elections. They donate to both parties so that they'll be treated well by whichever is elected.