Could you sum up who your are in 50 to 100 words? The chances are, if you have something published you will be asked to. Many magazines like to include a short paragraph about the writer after their work or on a contributors' page. Having a few basic sentences ready can save a lot of time.
    You need to show a little of your experience or what makes your writing different. There's no room for a CV. The information you include will probably be similar to what you would put in a cover letter, but even more condensed. Not having previous publications isn't a drawback. You could mention relevant training or work. For example, if your story is set in a department store, readers will be interested if you were inspired to write it because you used to work in one. If you have been published before, you could drop the names of a couple of the most prestigious publications and/or the widest ranging. Personalise you 'bio' by including a hint about how you live. Finally, if you have a website, book or something else to promote, such as the fact you give talks, make sure you mention it.
    Once you have the basics, tailor the bio to the particular publication. If it's a crime fiction magazine, your publishing record in women's magazines might not be as impressive as having studied law. Check the bios in earlier issues, if possible, to give you some ideas.
    I'd advise against being too zany, because you can guarantee that anything you put that's off the wall is the part that will appear out of context on any internet search. I speak from experience. One publication my work appeared in asked for a bio that included two false facts and one true one, now I keep seeing my name connected with weather vanes. I won't go into details, I wouldn't want to make things worse.