When someone is bombed, they have had so much alcohol, or such strong illegal drugs, that they can barely think, talk, or walk. Friends say it after a wild night: completely bombed, bombed out of their mind. It is informal slang, heard more in American talk than in careful British English, and it is not a polite word for class, work, or meeting someone's parents. The picture is that drink or drugs have knocked the person out, as if something heavy has hit them. People use it for both drink and drugs; tone and context tell you which. This is not the same as I bombed the test, which means you failed badly — that is another, later use of the same shape.