Write an opening that includes your name, a basic idea of what you do, a reference to your experience and talents, and an idea of why the reader needs your expertise.
Write about your accomplishments, not what you hope to do. Discussing plans does not identify why a reader should depend on your skills. Establishing your credibility is key and is done by citing your experience.
Be concise, simple and honest. Don't offer exaggeration, don't linger on one topic, and read what you've written and go back and trim where you can. For example, instead of "John Smith has done a lot in his career as a professional biography writer and hopes to put his skills to work for you in the same manner," you could write "John Smith enjoys a successful career as a biographer." The reader learns you do this for a living, so it's a given that you can help others.
Focus on your expertise, not your personal life. Naturally you'll want to give the reader a basic idea of you, but keep personal, subjective info to a minimum. That means don't include how wonderful your family is, how smart your dog is, how great the weather in San Diego is, for example. Think relevant and put yourself in the reader's place: What would you want to know about someone who claims to be an expert in something?
Consider this sample bio:
"John Smith graduated from Southern University in 1985 with a degree in communications. For several years, he has worked as a "Building Relationships" columnist for the Heritage Trust Publications in Arizona before relocating to Champaign, Illinois, to pursue graduate study in management and leadership. He completed a master of science in English literature from the University of Illinois in 2000. John has published two books: "Building a Team through Management Keys" and "Leadership Is Not Ownership," which garnered the prestigious "Golden Leader" award from the Association of Managers. John lives in Sante Fe."