You can apply to MBA programs with no "management" experience, but if you have no "work" experience then you're facing a tremendous uphill battle. Since you're in Missouri, you might want to check out Olin Business School at Washington University in St. Louis. WashU is one of the few schools that embraces applicants straight out of undergrad, and about 15% of the enrolled class are in this pool which is called "Young Leaders." The Young Leaders pool numbers are 3.6 GPA, 722 GMAT. And a little hint with Olin: take the GMAT, and if you score 700+ use it in your application, and if not, use your GRE score.
The trouble with Olin, however, is that there's no way to get a single-campus double in public policy. You could do 2 years at Olin, and then a 1-year masters at somewhere like Harris or Maxwell though.
If you're in KC, especially if you're at UMKC, send me a PM if you want to chat about the MBA side.