Yes, I would think she was saying she wore something that showed off her bosom to the greatest advantage or allure. And no, you can't leave "something" out of the sentence. Something is the object .. she always wore something. Booby modifies the something.
Booby is a word in its own right, but not in this sense (it's a stupid person, or a type of bird). It is clearly understood here, however, and some dictionaries will list it in the sense of a female breast as "vulgar." It's not a "dirty word" however. Just slangy.