I hate to tell you but what everyone else is telling you is true. It is next to impossible finding a one bedroom apartment in that range. Maybe if you increase your budget a bit, I can help you find a nice little apartment in Brooklyn, but certainly not in Manhattan.
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I agree with Sharon. Standard one bedrooms are priced higher than that. You may run across a rent stabilized unit every now and again that below market price but that's a needle in a haystack. In addition to considering a roommate, I would also suggest checking into the housing lotteries which could offer you more affordable options. Here's the link in case you need it. I wish you the very best in your search for a new home. http://www.nyc.gov/html/hpd/html/apartment/apartment.shtml
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