The word "bittersweet" is not an example of antithesis; however, it is a great example of oxymoron. An oxymoron is a figure of speech that combines contrasting terms for effect. So, because the separate terms "bitter" and "sweet" contrast each other, their combination creates an oxymoron.
An example of antithesis is seen in the following line from Mark Twain's essay "The Lowest Animal": "The cat is innocent, Man is not." An antithesis is a rhetorical device in which parallel structure is used to juxtapose two contrasting ideas. The line from Twain's essay juxtaposes the innocence of cats with the innocence of humans to suggest that the cat naturally has this character trait, while man/woman does not. Writers use antithesis to highlight claims and statements through contrast.