Oh, this is an expression used in relationships, and is most frequently said to women who have a lazy or abusive boyfriend/husband. It means get rid of him, break up with him, dump him.

It's exactly as Andi explained. I'll just clarify a couple of parts. A "bum" can mean a hobo or a layabout. Generally a person who does nothing except sit on their own bum. "To dump" means to reject or get rid of something. Drop it on the rubbish heap. For relationships, this means one person chooses to end the relationship.