Think about what you want to include in your one-paragraph bio. One paragraph will typically be between five and ten lines. If the bio is going to be printed in a magazine, there may be a word count associated with the bio, depending upon the magazine's guideline preferences. Find essential information you need to include in your brief bio to give readers an accurate overview of who you are.
Give the impression someone else is writing the bio. Write in the third person. Though this is autobiographical, the standard typically calls for third-person writing. Some magazines don't object to first person. If this is the case, you can write in first person, though when you write in first person you may sound as if you're bragging about yourself. Third-person makes your credentials and accomplishments appear to be more impressive. It always sounds better if someone else talks about your achievements.
Capture the essence of your career, your educational background, and your awards and other recognition. Avoid using words you don't need to. "After attending the School of Arts in Boston, Joe went on to paint . . ." is wordy. Try "Joe attended Boston School of Arts. His work includes . . ." This is a substantial reduction in word count, which leaves you room to highlight your accomplishments. If you're a writer, artist, or performer who needs to list published credits, be selective of the work you include. Stick with career highlights.