I would recommend using BisManOnline http://(www.bismanonline.com) to find a rental - it's a local classifieds site much like Craigslist but it's well maintained and monitored. BisManOnline is the king of local classifieds and, because of that, very few locals use Craigslist for anything - so I'd steer away from Craigslist or any other national site as such.
Below is a list of reputable rental companies in Bismarck (most of these are apartments though, not houses).
Simply type in the house number (not the street or anything else) and it will give you a list of properties in Bismarck with that house number. Click on the proper one and it will give you the owner on record. Of course, there is a chance that the property could have changed hands recently and the records haven't been update yet, but more than likely it should be correct.
1. Do NOT provide personal info and/or $$$ unless the person you're sending it to for review (either directly or through their agent) is actually the person on title.
2. Contact a local RE agent that can answer your questions and find the needs you're wanting to be met with your future home. He or she should be able to provide you a list of bona fide homes that are actually available.
3. If it sounds too good to be true, it probably is.