Writing a succinct bio is a little like Tweeting. As I said in the post on cover letters (Take Cover), editors want to get their work done and go home or go out for a beer or anywhere but the office, if they have offices. (I think most of the people in my local coffee shop are poetry editors looking for a home.) When submission guidelines ask that you include a bio, they often say how many words they want, and it's not many. The safe thing to do is read the bios in the current issue of whatever market you plan to send poems to. You'll quickly get a sense of their style.
Some bios, usually found on the contributors' page, are funny but don't tell you much about the writer as writer. They tell you about the family dog, the wacky diet, or the esoteric day job, like worm farming. Others will be very dry and to the point: education, day job, previous publications. Lately more and more writers include their website. (More on that another day.) Easy-peasy, lemon squeezy. But what if you dropped out of school in kindergarten and have not yet published a word? Well, you'll have to come up with something. Often the state or region where you live, what you do to earn your bread--assuming it's legal or you're not in the witness protection program--and a line about how you became interested in poetry. You might mention a favorite poet, if he or she is well known enough to lend some credence to your fanship.
I paste my standard bio into the cover letter. If the market asks that you use an electronic submission site, like Submishmash, use the comment portion of that site to include your bio. No fancy fonts, just the facts. Now, go, submit. It won't hurt a bit. Tee hee.