Will I still have a chance at attending this school with 4 bs (2 bs and 2 b+) on my otherwise A/A- transcript?
If the Ohio State University of Columbus does not accept you, Ohio State University of Newark/Manfield etc. will certainly do so.
Seriously, seems like your GPA is 3.6+, which should be fine (obviously it is one of many factors in admisions). But no one refers to the school as Ohio State University of Columbus!