Yeah, the rental companies do cater to college students in BG....and, even worse, it is nearly impossible to find a place in BG and the area that allows cats! Have you tried this property?
T & R Properties - Arbors of Bowling Green
Just did a search on BG rentals and I don't think they actively try to recruit students. It's kind of south of the city and away from campus - a good location.
If you are having no luck, Perrysburg is a great city that's about 10 minutes from BG and doesn't cater to students as much.